BASIC ALGEBRA PROBLEMS
Mr. X helps math students better understand Basic Algebra. Our sample math problems are designed to provide the necessary practice to know and understand the ideas and principles of basic algebra. The sample problems reinforce the basic algebra lessons available to our subscribers. Check out our free samples below, as well as the basic algebra problem set.
Basic Algebra Sample Problem 1
Basic Algebra Sample Problem 2
Basic Algebra Problems
Algebraic Expressions
Words to Algebraic Expressions 


Title/Subject  Description  
Writing Variable Expressions Problem Set 1  We translate word phrases into algebraic expression. In this problem set our expressions are either one or two term expressions with one variable. 

Writing Variable Expressions Problem Set 2  We translate word phrases into algebraic expression. In this problem set our expressions are either one or two term expressions with one variable. 

Writing Variable Expressions Problem Set 3  We translate word phrases into algebraic expression. In this problem set our expressions are either one or two term expressions with one variable. 

Writing Variable Expressions Problem Set 4  We translate word phrases into algebraic expression. In this problem set our expressions are either two or three term expressions with two variables. 

Writing Variable Expressions Problem Set 5  Writing English into Mathematics takes practice. To write the language effectively takes much practice. 

Translate Phrases 

Title/Subject  Description  
Translate Phrases Problem Set 1  A basic worksheet with ten problems to translate English into math. This is basic algebra. 

Translate Phrases Problem Set 2  We raise the difficulty level of this worksheet. We are required to translate algebraic expressions with two real values and one variable. 

Translate Phrases Problem Set 3  Another moderate worksheet where the problems have one variables and two terms.  
Translate Phrases Problem Set 4  A harder worksheet for translating phrases. Our phrases now include two variables. 

Simplifying Variables 

Title/Subject  Description  
Combining Like Terms Problem Set 1  We distribute values that appear directly in front of parentheses. We multiply those leading factors across the terms within the parentheses. This is called distribution. 

Combining Like Terms Problem Set 2  We distribute values by multiplying times values within parentheses. We multiply those leading factors across the terms within the parentheses. This is called distribution. 

The Distributive Property 

Title/Subject  Description  
The Distributive Property Problem Set 1  We distribute a number in front of parentheses. We multiply that leading value times each term within the parentheses. 

The Distributive Property Problem Set 2  We distribute a number in front of parentheses. We multiply that leading value times each term within the parentheses. 

Evaluating One Variable 

Title/Subject  Description  
Algebraic Expressions Evaluating One Variable Problem Set 1  Evaluations in early Basic Algebra are very important. These early lessons are essential to getting comfortable with higher mathematics. Algebra is easy if you understand Arithmetic. 

Evaluating Two Variables 

Title/Subject  Description  
Simplifying Algebraic Expressions Problem Set 1  We evaluate algebraic expressions consisting of two, three or four terms. We either add or subtract the terms. 

Simplifying Algebraic Expressions Problem Set 2  We evaluate algebraic expressions consisting of two, three or four terms. We increase the difficulty by including multiplication and division as possible operations. 

Simplifying Algebraic Expressions Problem Set 3  We evaluate algebraic expressions consisting of two, three or four terms. We increase the difficulty by including multiplication and division as possible operations. 
Basic Skills
Writing Variable Expressions 


Title/Subject  Description  
Writing Variable Expressions Problem Set 1  We translate word phrases into algebraic expression. In this problem set our expressions are either one or two term expressions with one variable. 

Writing Variable Expressions Problem Set 2  We translate word phrases into algebraic expression. In this problem set our expressions are either one or two term expressions with one variable. 

Writing Variable Expressions Problem Set 3  We translate word phrases into algebraic expression. In this problem set our expressions are either one or two term expressions with one variable. 

Writing Variable Expressions Problem Set 4  We translate word phrases into algebraic expression. In this problem set our expressions are either two or three term expressions with two variables. 

Writing Variable Expressions Problem Set 5  Writing English into Mathematics takes practice. To write the language effectively takes much practice. 

Order of Operations 

Title/Subject  Description  
Order of Operations Problem Set 1  We use the order of operations or PEMDAS to solve problems that have 4 numbers and three operations.  
Order of Operations Problem Set 2  We use the order of operations or PEMDAS to solve problems that have 5 numbers and four operations.  
Order of Operations Problem Set 3  We use the order of operations or PEMDAS to solve problems that have 5 numbers and four operations.  
Evaluating Expressions 

Title/Subject  Description  
Simplifying Algebraic Expressions Problem Set 1  We evaluate algebraic expressions consisting of two, three or four terms. We either add or subtract the terms. 

Simplifying Algebraic Expressions Problem Set 2  We evaluate algebraic expressions consisting of two, three or four terms. We increase the difficulty by including multiplication and division as possible operations. 

Simplifying Algebraic Expressions Problem Set 3  We evaluate algebraic expressions consisting of two, three or four terms. We increase the difficulty by including multiplication and division as possible operations. 

Identifying Number Sets 

Title/Subject  Description  
Identifying Number Sets Problem Set  Which number sets to the following expressions belong to? Answers include Integers, Whole Numbers, Real Numbers, Natural Numbers, Rational Numbers, and Irrational Numbers.  
Identifying Number Sets Problem Set 2  Identify real values as belonging to the sets of: Rational Numbers or Irrational Numbers; Natural Numbers; Whole Numbers, or Integers.  
Adding and Subtracting Rational Numbers 

Title/Subject  Description  
Adding and Subtracting Rational Numbers Problem Set 1  We work problems with rational values with integers of both positive and negative values. 

Adding and Subtracting Rational Numbers Problem Set 2  We work problems with rational values, including fractions, decimals, and integers, with both positive and negative values. This part of the language requires lots of practice so that its manipulation can be almost absentminded, or secondnature to the student. 

Adding And Subtracting Rational Numbers Problem Set 3  We add rational numbers, positive and negative, as integers, and decimals and fractions. It's the Arithmetic of Basic Algebra. 

Multiplying and Dividing Rational Numbers 

Title/Subject  Description  
Multiplying and Dividing Rational Numbers Problem Set  We multiply and divide rational values as Integers and Fractions. You MUST know your basic facts of multiplication. It's the Arithmetic of Basic Algebra. 

The Distributive Property 

Title/Subject  Description  
The Distributive Property Problem Set 1  We distribute a number in front of parentheses. We multiply that leading value times each term within the parentheses. 

The Distributive Property Problem Set 2  We distribute a number in front of parentheses. We multiply that leading value times each term within the parentheses. 

Combining Like Terms 

Title/Subject  Description  
Combining Like Terms Problem Set 1  We distribute values that appear directly in front of parentheses. We multiply those leading factors across the terms within the parentheses. This is called distribution. 

Combining Like Terms Problem Set 2  We distribute values by multiplying times values within parentheses. We multiply those leading factors across the terms within the parentheses. This is called distribution. 

Percent of Change 

Title/Subject  Description  
Percent of Change 3  Facility and ease with these types of basic calculations are important. So practice. 

Percent of Change 4  Let us continue with practice in these basic calculations involving Percents.  
Percent of Change 5  Please don't get in a hurry with these basic calculations. Your practice needs to be thoughtful and deliberate. Thank you. 
Equations
One Step Equations with Integers 


Title/Subject  Description  
OneStep Equations with Integers  Take your times with these early lessons. Don't rush past them in some effort to "get the answer." Relax, and learn these basic principles; they are important to what comes later. 

Solving Basic Equations 01  Simple and straightforward algebraic expressions with a single variable. This is a great place to begin working algebra problems. 

Solving Basic Equations 02  Simple and straightforward algebraic expressions with a single variable. This is a great place to begin working algebra problems. 

One Step Equations with Decimals 

Title/Subject  Description  
OneStep Equations with Decimals  A lesson in some very basic algebra. It's good to get a lot of practice with these easy equations early in your study of Algebra. 

One Step Equations with Fractions 

Title/Subject  Description  
OneStep Equations with Fractions, Lesson 2  Don't rush pass these basics. These skills need to be practiced so that the manipulation of terms is easy and nearly automatic. 

Solving Basic Equations 03  Simple and straightforward algebraic expressions with a single variable. This is a great place to begin working algebra problems. 

Solving Basic Equations 04  Simple and straightforward algebraic expressions with a single variable. This is a great place to begin working algebra problems. 

One Step Equations Word Problems 

Title/Subject  Description  
One Step Equation Word Problems Problem Set 1  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 2  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 3  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 4  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 5  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 6  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
Two Step Equations with Integers 

Title/Subject  Description  
Solving Basic Equations 05  We soon discover that understanding (knowing) the basic facts of multiplication helps us greatly in soling algebraic equations. We also treat both sides of an equation identically, to simplify our lives. 

Solving Basic Equations 07  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Solving Basic Equations 08  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Solving Basic Equations 10  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Solving Basic Equations 12  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Two Step Equations with Decimals 

Title/Subject  Description  
Two Step Equations with Decimals Problem Set 1  Solve for the unknown. We solve the equation for the value that makes the statement true. 

Two Step Equations Word Problems 

Title/Subject  Description  
Two Step Equation Word Problems Paired Worksheet  Work along Mr. X solving two step equation word problems. Download the worksheet before you play the video! 

Two Step Equation Word Problems Sample Problem 1  An illustrative example: The sum of two numbers is 60, and the greater is four times the less. What are the numbers? 

Two Step Equation Word Problems Sample Problem 2  A man bought a horse and carriage for $500, paying three times as much for the carriage as for the horse. How much did each cost? 

Two Step Equation Word Problems Sample Problem 3  For 72 cents Martha bought some needles and thread, paying eight times as much for the thread as for the needles. How much did she pay for each? 

Two Step Equation Word Problems Sample Problem 4  An illustrative example: What number added to twice itself and 40 more will make a sum equal to eight times the number?  
Two Step Equation Word Problems Sample Problem 5  James is 3 years older than William, and twice James's age is equal to three times William's age. What is the age of each? 

Two Step Equation Word Problems Sample Problem 6  Roger is onefourth as old as his father, and the sum of their ages is 70 years. How old is each? 

Two Step Equation Word Problems Sample Problem 7  An illustrative example: If the difference between two numbers is 48, and one number is five times the other, what are the numbers?  
Two Step Equation Word Problems Sample Problem 8  James gathered 12 quarts of nuts more than Henry gathered. How many did each gather if James gathered three times as many as Henry? 

Two Step Equation Word Problems Sample Problem 9  Mr. A is 48 years older than his son, but he is only three times as old. How old is each? 

Two Step Equation Word Problems Sample Problem 10  A man bought a hat, a pair of boots, and a necktie for $$7.50; the hat cost four times as much as the necktie, and the boots cost five times as much as the necktie. What was the cost of each? 

Two Step Equation Word Problems Sample Problem 11  There are 120 pigeons in three flocks. In the second there are three times as many as in the first, and in the third as many as in the first and second combined. How many pigeons in each flock? 

Two Step Equation Word Problems Sample Problem 12  Three men, A, B, and C, earned $110; A earned four times as much as B, and C as much as both A and B. How much did each earn? 

Two Step Equation Word Problems Sample Problem 13  A farmer bought a horse, a cow, and a calf for $72; the cow cost twice as much as the calf, and the horse three times as much as the cow. What was the cost of each? 

Two Step Equation Word Problems Sample Problem 14  A grocer sold one pound of tea and two pounds of coffee for $1.50, and the price of the tea per pound was three times that of the coffee. What was the price of each? 

Two Step Equation Word Problems Sample Problem 15  By will Mrs. Cabot was to receive five times as much as her son Henry. If Henry received $20,000 less than his mother, how much did each receive? 

Two Step Equation Word Problems Sample Problem 16  An illustrative example: Divide the number 126 into two parts such that one part is 8 more than the other.  
Two Step Equation Word Problems Sample Problem 17  At an election in which 1079 votes were cast the successful candidate had a majority of 95. How many votes did each of the two candidates receive? 

Two Step Equation Word Problems Sample Problem 18  John and Henry together have 143 marbles. If I should give Henry 15 more, he would have just as many as John. How many has each? 

Two Step Equation Word Problems Sample Problem 19  Two men whose wages differ by eight dollars receive both together $44 per hour. How much does each receive? 

Two Step Equation Word Problems Sample Problem 20  Divide 62 into three parts such that the first part is 4 more than the second, and the third 7 more than the second.  
Two Step Equation Word Problems Sample Problem 21  A man had 95 sheep in three flocks. In the first flock there were 23 more than in the second, and in the third flock 12 less than in the second. How many sheep in each flock? 

Two Step Equation Word Problems Sample Problem 22  A man owns three farms. In the first there are 5 acres more than in the second and 7 acres less than in the third. If there are 53 acres in all the farms together, how many acres are there in each farm? 

Two Step Equation Word Problems Sample Problem 23  Three firms lost $118,000 by fire. The second firm lost $6000 less than the first and $20,000 more than the third. What was each firm's loss? 

Two Step Equation Word Problems Sample Problem 24  In an orchard containing 33 trees the number of pear trees is 5 more than three times the number of apple trees. How many are there of each kind? 

Two Step Equation Word Problems Sample Problem 25  To the double of a number I add 17 and obtain as a result 147. What is the number? Also: To four times a number I add 23 and obtain 95. Also: From three times a number I take 25 and obtain 47. Also: Find a number which being multiplied by 5 and having 14 added to the product will equal 69. 

Two Step Equation Word Problems Sample Problem 26  I bought some tea and coffee for $10.39. If I paid for the tea 61 cents more than five times as much as for the coffee, how much did I pay for each? 

Two Step Equation Word Problems Sample Problem 27  Two houses together contain 48 rooms. If the second house has 3 more than twice as many rooms as the first, how many rooms has each house? 

Two Step Equation Word Problems Sample Problem 28  Mr. Ames builds three houses. The first cost $2000 more than the second, and the third twice as much as the first. If they all together cost $18,000, what was the cost of each house? 

Two Step Equation Word Problems Sample Problem 29  George bought an equal number of apples, oranges, and bananas for $1.08; each apple cost 2 cents, each orange 4 cents, and each banana 3 cents. How many of each did he buy? 

Two Step Equation Word Problems Sample Problem 30  A man bought 3 lamps and 2 vases for $6. If a vase cost 50 cents less than 2 lamps, what was the price of each? 

Two Step Equation Word Problems Sample Problem 31  Johnson and May enter into a partnership in which Johnson's interest is four times as great as May's. Johnson's profit was $4500 more than May's profit. What was the profit of each? 

Two Step Equation Word Problems Sample Problem 32  Divide 71 into three parts so that the second part shall be 5 more than four times the first part, and the third part three times the second.  
Two Step Equation Word Problems Sample Problem 33  I bought a certain number of barrels of apples and three times as many boxes of oranges for $33. I paid $2 a barrel for the apples, and $3 a box for the oranges. How many of each did I buy? 

Two Step Equation Word Problems Sample Problem 34  Divide the number 288 into three parts, so that the third part shall be twice the second, and the second five times the first.  
Two Step Equation Word Problems Sample Problem 35  If John's age be multiplied by 5, and if 24 be added to the product, the sum will be seven times his age. What is his age? 

Two Step Equation Word Problems Sample Problem 36  A man, being asked how many sheep he had, said, "If you will give me 24 more than six times what I have now, I shall have ten times my present number." How many had he?  
Two Step Equation Word Problems Sample Problem 37  Four dozen oranges cost as much as 7 dozen apples, and a dozen oranges cost 15 cents more than a dozen apples. What is the price of each? 

Two Step Equation Word Problems Sample Problem 38  A farmer pays just as much for 4 horses as he does for 6 cows. If a cow costs 15 dollars less than a horse, what is the cost of each? 

Two Step Equation Word Problems Sample Problem 39  Roger is onefourth as old as his father, and the sum of their ages is 70 years. How old is each? 

Two Step Equation Word Problems Sample Problem 40  Jane is onefifth as old as Mary, and the difference of their ages is 12 years. How old is each? 

Two Step Equation Word Problems Sample Problem 41  Two men own a third and twofifths of a mill respectively. If their part of the property is worth $22,000, what is the value of the mill? 

Two Step Equation Word Problems Sample Problem 42  In three pastures there are 42 cows. In the second there are twice as many as in the first, and in the third there are onehalf as many as in the first. how many cows are there in each pasture? 

Two Step Equation Word Problems Sample Problem 43  What number increased by threesevenths of itself will amount to 8640?  
Two Step Equation Word Problems Sample Problem 44  There are three numbers whose sum is 90; the second is equal to onehalf of the first, and the third is equal to the second plus three times the first. What are the numbers? 

Two Step Equation Word Problems Sample Problem 45  A grocer sold 62 pounds of tea, coffee, and cocoa. Of tea he sold 2 pounds more than of coffee, and of cocoa 4 pounds more than of tea. How many pounds of each did he sell? 

Two Step Equation Word Problems Sample Problem 46  John has oneninth as much money as Peter, but if his father should give him 72 cents, he would have just the same as Peter. How much money has each boy? 

Two Step Equation Word Problems Sample Problem 47  Two boys picked 26 boxes of strawberries. If John picked fiveeighths as many as Henry, how many boxes did each pick? 

Two Step Equation Word Problems Sample Problem 48  In a school containing 420 pupils, there are threefourths as many boys as girls. How many are there of each? 

Two Step Equation Word Problems Sample Problem 49  One man carried off threesevenths of a pile of soil, another man fourninths of the pile. In all they took 110 cubic yards of earth. How large was the pile at first? 

Two Step Equation Word Problems Sample Problem 50  Matthew had three times as many stamps as Herman, but after he had lost 70, and Herman had bought 90, they put what they had together and found that they had 540 stamps. How many had each at first? 

Multiple Step Equations with Integers 

Title/Subject  Description  
Solve Linear Equations Problem Set 01  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solve Linear Equations Problem Set 02  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solve Linear Equations Problem Set 03  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solve Linear Equations Problem Set 04  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solve Linear Equations Problem Set 05  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solving Basic Equations 06  We soon discover that understanding (knowing) the basic facts of multiplication helps us greatly in soling algebraic equations. We also treat both sides of an equation identically, to simplify our lives. 

Solving Basic Equations 09  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Multiple Step Equations with Decimals and Fractions 

Title/Subject  Description  
Solve Linear Equations with Fractions Problem Set 01  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 

Solve Linear Equations with Fractions Problem Set 02  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 

Solve Linear Equations with Fractions Problem Set 03  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 

Solve Linear Equations with Fractions Problem Set 04  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 
Equations
One Step Equations with Integers 


Title/Subject  Description  
Solving Basic Equations 01  Simple and straightforward algebraic expressions with a single variable. This is a great place to begin working algebra problems. 

Solving Basic Equations 02  Simple and straightforward algebraic expressions with a single variable. This is a great place to begin working algebra problems. 

OneStep Equations with Integers  Take your time with these early lessons. Don't rush past them in some effort to "get the answer." Relax, and learn these basic principles; they are important to what comes later. 

One Step Equations with Decimals 

Title/Subject  Description  
OneStep Equations with Decimals  A lesson in some very basic algebra. It's good to get a lot of practice with these easy equations early in your study of Algebra. 

One Step Equations with Fractions 

Title/Subject  Description  
OneStep Equations with Fractions, Lesson 2  Don't rush pass these basics. These skills need to be practiced so that the manipulation of terms is easy and nearly automatic. 

Solving Basic Equations 03  Simple and straightforward algebraic expressions with a single variable. This is a great place to begin working algebra problems. 

Solving Basic Equations 04  Simple and straightforward algebraic expressions with a single variable. This is a great place to begin working algebra problems. 

One Step Equations with Integers, Decimals, & Fractions 

Title/Subject  Description  
Solving Basic Equations 11  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Solving Basic Equations 13  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Two Step Equations with Integers 

Title/Subject  Description  
Solving Basic Equations 05  We soon discover that understanding (knowing) the basic facts of multiplication helps us greatly in soling algebraic equations. We also treat both sides of an equation identically, to simplify our lives. 

Solving Basic Equations 07  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Solving Basic Equations 08  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Solving Basic Equations 10  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Solving Basic Equations 12  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Two Step Equations with Decimals 

Title/Subject  Description  
Two Step Equations with Decimals Problem Set 1  Solve for the unknown. We solve the equation for the value that makes the statement true. 

Multiple Step Equations with Integers 

Title/Subject  Description  
Solve Linear Equations Problem Set 01  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solve Linear Equations Problem Set 02  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solve Linear Equations Problem Set 03  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solve Linear Equations Problem Set 04  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solve Linear Equations Problem Set 05  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solving Basic Equations 06  We soon discover that understanding (knowing) the basic facts of multiplication helps us greatly in soling algebraic equations. We also treat both sides of an equation identically, to simplify our lives. 

Solving Basic Equations 09  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Multiple Step Equations with Decimals and Fractions 

Title/Subject  Description  
Solve Linear Equations with Fractions Problem Set 01  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 

Solve Linear Equations with Fractions Problem Set 02  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 

Solve Linear Equations with Fractions Problem Set 03  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 

Solve Linear Equations with Fractions Problem Set 04  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 

Absolute Value 

Title/Subject  Description  
Absolute Value  Monomial Expressions  Problem Set 1  The idea of Absolute Value is reinforced with basic problems.  
Absolute Value  Polynomial Expressions with no Coefficients  Problem Set 1  Absolute Value is an important idea. Practice this until you're very comfortable with it. 

Absolute Value  Polynomial Expressions with Coefficients  Problem Set 1  Sometimes solving two little equations is easier than solving one big one. Some problems with Absolute Value lend themselves to that approach. 

Absolute Value  Monomial Fractional Expressions  Problem Set 1  More work with Absolute Value involves reciprocals. Reciprocals make these types of problems very easy to manipulate and to solve. 

Absolute Value  Polynomial Fractional Expressions  Problem Set 1  Reciprocals are very helpful in solving some equations with Absolute Value. This is good practice for a variety of skills. 

Absolute Value  Polynomial Expressions with Fractions  Problem Set 1  Each of our expressions have two values for the unknown that make the statement true. Reciprocals make some of our calculations very easy. 

Solving Proportions 

Title/Subject  Description  
Solving Proportions Problem Set 1  Solving Proportions with Monomial Variable Expressions. We solve proportions with monomial variable expressions on each side of the equation. Very easy, if you know your arithmetic. 

Solving Proportions Problem Set 2  Solving Proportions with Polynomial Variable Expressions with no Coefficients. Moving tomatoes is faster and more efficient than multiplying both sides of the equation by the same value. But that is rather what we do to solve these equations. 

Solving Proportions Problem Set 3  Solving Proportions with Polynomial Variable Expressions with Coefficients. We recommend learning how to "move tomatoes." If you're comfortable with arithmetic, basic algebra is a snap! 

Solving Proportions Problem Set 4  Solving Proportions with two variable expressions (1 polynomial, 1 monomial). The calculations in this video are especially easy and straightforward if you can "move tomatoes." 

Solving Proportions Problem Set 5  Solving Proportions with two variable expressions (2 polynomials). If you've picked up on the idea of moving tomatoes, you're going to find these problems easy to solve. 

Percent Problems 

Title/Subject  Description  
Percent Problems Sample Problems 1  A few calculations with multiplication and division, with both decimal values and percents.  
One Step Equation Word Problems 

Title/Subject  Description  
One Step Equation Word Problems Problem Set 1  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 2  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 3  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 4  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 5  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 6  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
Two Step Equation Word Problems 

Title/Subject  Description  
Two Step Equation Word Problems Paired Worksheet  Work along Mr. X solving two step equation word problems. Download the worksheet before you play the video! 

Two Step Equation Word Problems Sample Problem 1  An illustrative example: The sum of two numbers is 60, and the greater is four times the less. What are the numbers? 

Two Step Equation Word Problems Sample Problem 2  A man bought a horse and carriage for $500, paying three times as much for the carriage as for the horse. How much did each cost? 

Two Step Equation Word Problems Sample Problem 3  For 72 cents Martha bought some needles and thread, paying eight times as much for the thread as for the needles. How much did she pay for each? 

Two Step Equation Word Problems Sample Problem 4  An illustrative example: What number added to twice itself and 40 more will make a sum equal to eight times the number?  
Two Step Equation Word Problems Sample Problem 5  James is 3 years older than William, and twice James's age is equal to three times William's age. What is the age of each? 

Two Step Equation Word Problems Sample Problem 6  Roger is onefourth as old as his father, and the sum of their ages is 70 years. How old is each? 

Two Step Equation Word Problems Sample Problem 7  An illustrative example: If the difference between two numbers is 48, and one number is five times the other, what are the numbers?  
Two Step Equation Word Problems Sample Problem 8  James gathered 12 quarts of nuts more than Henry gathered. How many did each gather if James gathered three times as many as Henry? 

Two Step Equation Word Problems Sample Problem 9  Mr. A is 48 years older than his son, but he is only three times as old. How old is each? 

Two Step Equation Word Problems Sample Problem 10  A man bought a hat, a pair of boots, and a necktie for $$7.50; the hat cost four times as much as the necktie, and the boots cost five times as much as the necktie. What was the cost of each? 

Two Step Equation Word Problems Sample Problem 11  There are 120 pigeons in three flocks. In the second there are three times as many as in the first, and in the third as many as in the first and second combined. How many pigeons in each flock? 

Two Step Equation Word Problems Sample Problem 12  Three men, A, B, and C, earned $110; A earned four times as much as B, and C as much as both A and B. How much did each earn? 

Two Step Equation Word Problems Sample Problem 13  A farmer bought a horse, a cow, and a calf for $72; the cow cost twice as much as the calf, and the horse three times as much as the cow. What was the cost of each? 

Two Step Equation Word Problems Sample Problem 14  A grocer sold one pound of tea and two pounds of coffee for $1.50, and the price of the tea per pound was three times that of the coffee. What was the price of each? 

Two Step Equation Word Problems Sample Problem 15  By will Mrs. Cabot was to receive five times as much as her son Henry. If Henry received $20,000 less than his mother, how much did each receive? 

Two Step Equation Word Problems Sample Problem 16  An illustrative example: Divide the number 126 into two parts such that one part is 8 more than the other.  
Two Step Equation Word Problems Sample Problem 17  At an election in which 1079 votes were cast the successful candidate had a majority of 95. How many votes did each of the two candidates receive? 

Two Step Equation Word Problems Sample Problem 18  John and Henry together have 143 marbles. If I should give Henry 15 more, he would have just as many as John. How many has each? 

Two Step Equation Word Problems Sample Problem 19  Two men whose wages differ by eight dollars receive both together $44 per hour. How much does each receive? 

Two Step Equation Word Problems Sample Problem 20  Divide 62 into three parts such that the first part is 4 more than the second, and the third 7 more than the second.  
Two Step Equation Word Problems Sample Problem 21  A man had 95 sheep in three flocks. In the first flock there were 23 more than in the second, and in the third flock 12 less than in the second. How many sheep in each flock? 

Two Step Equation Word Problems Sample Problem 22  A man owns three farms. In the first there are 5 acres more than in the second and 7 acres less than in the third. If there are 53 acres in all the farms together, how many acres are there in each farm? 

Two Step Equation Word Problems Sample Problem 23  Three firms lost $118,000 by fire. The second firm lost $6000 less than the first and $20,000 more than the third. What was each firm's loss? 

Two Step Equation Word Problems Sample Problem 24  In an orchard containing 33 trees the number of pear trees is 5 more than three times the number of apple trees. How many are there of each kind? 

Two Step Equation Word Problems Sample Problem 25  To the double of a number I add 17 and obtain as a result 147. What is the number? Also: To four times a number I add 23 and obtain 95. Also: From three times a number I take 25 and obtain 47. Also: Find a number which being multiplied by 5 and having 14 added to the product will equal 69. 

Two Step Equation Word Problems Sample Problem 26  I bought some tea and coffee for $10.39. If I paid for the tea 61 cents more than five times as much as for the coffee, how much did I pay for each? 

Two Step Equation Word Problems Sample Problem 27  Two houses together contain 48 rooms. If the second house has 3 more than twice as many rooms as the first, how many rooms has each house? 

Two Step Equation Word Problems Sample Problem 28  Mr. Ames builds three houses. The first cost $2000 more than the second, and the third twice as much as the first. If they all together cost $18,000, what was the cost of each house? 

Two Step Equation Word Problems Sample Problem 29  George bought an equal number of apples, oranges, and bananas for $1.08; each apple cost 2 cents, each orange 4 cents, and each banana 3 cents. How many of each did he buy? 

Two Step Equation Word Problems Sample Problem 30  A man bought 3 lamps and 2 vases for $6. If a vase cost 50 cents less than 2 lamps, what was the price of each? 

Two Step Equation Word Problems Sample Problem 31  Johnson and May enter into a partnership in which Johnson's interest is four times as great as May's. Johnson's profit was $4500 more than May's profit. What was the profit of each? 

Two Step Equation Word Problems Sample Problem 32  Divide 71 into three parts so that the second part shall be 5 more than four times the first part, and the third part three times the second.  
Two Step Equation Word Problems Sample Problem 33  I bought a certain number of barrels of apples and three times as many boxes of oranges for $33. I paid $2 a barrel for the apples, and $3 a box for the oranges. How many of each did I buy? 

Two Step Equation Word Problems Sample Problem 34  Divide the number 288 into three parts, so that the third part shall be twice the second, and the second five times the first.  
Two Step Equation Word Problems Sample Problem 35  If John's age be multiplied by 5, and if 24 be added to the product, the sum will be seven times his age. What is his age? 

Two Step Equation Word Problems Sample Problem 36  A man, being asked how many sheep he had, said, "If you will give me 24 more than six times what I have now, I shall have ten times my present number." How many had he?  
Two Step Equation Word Problems Sample Problem 37  Four dozen oranges cost as much as 7 dozen apples, and a dozen oranges cost 15 cents more than a dozen apples. What is the price of each? 

Two Step Equation Word Problems Sample Problem 38  A farmer pays just as much for 4 horses as he does for 6 cows. If a cow costs 15 dollars less than a horse, what is the cost of each? 

Two Step Equation Word Problems Sample Problem 39  Roger is onefourth as old as his father, and the sum of their ages is 70 years. How old is each? 

Two Step Equation Word Problems Sample Problem 40  Jane is onefifth as old as Mary, and the difference of their ages is 12 years. How old is each? 

Two Step Equation Word Problems Sample Problem 41  Two men own a third and twofifths of a mill respectively. If their part of the property is worth $22,000, what is the value of the mill? 

Two Step Equation Word Problems Sample Problem 42  In three pastures there are 42 cows. In the second there are twice as many as in the first, and in the third there are onehalf as many as in the first. how many cows are there in each pasture? 

Two Step Equation Word Problems Sample Problem 43  What number increased by threesevenths of itself will amount to 8640?  
Two Step Equation Word Problems Sample Problem 44  There are three numbers whose sum is 90; the second is equal to onehalf of the first, and the third is equal to the second plus three times the first. What are the numbers? 

Two Step Equation Word Problems Sample Problem 45  A grocer sold 62 pounds of tea, coffee, and cocoa. Of tea he sold 2 pounds more than of coffee, and of cocoa 4 pounds more than of tea. How many pounds of each did he sell? 

Two Step Equation Word Problems Sample Problem 46  John has oneninth as much money as Peter, but if his father should give him 72 cents, he would have just the same as Peter. How much money has each boy? 

Two Step Equation Word Problems Sample Problem 47  Two boys picked 26 boxes of strawberries. If John picked fiveeighths as many as Henry, how many boxes did each pick? 

Two Step Equation Word Problems Sample Problem 48  In a school containing 420 pupils, there are threefourths as many boys as girls. How many are there of each? 

Two Step Equation Word Problems Sample Problem 49  One man carried off threesevenths of a pile of soil, another man fourninths of the pile. In all they took 110 cubic yards of earth. How large was the pile at first? 

Two Step Equation Word Problems Sample Problem 50  Matthew had three times as many stamps as Herman, but after he had lost 70, and Herman had bought 90, they put what they had together and found that they had 540 stamps. How many had each at first? 

Distance, Rate, and Time Word Problems 

Title/Subject  Description  
Distance, Rate, and Time Word Problems 1  Distance equals Rate times Time. This basic relationship needs to be reinforced with lots of practice. 

Distance, Rate, and Time Word Problems 2  Distance equals Rate times Time. Distance divided by Rate equals Time. Distance divided by Time is the Rate, or Speed. 

Work Word Problems 

Title/Subject  Description  
Solving Basic Equations 08  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Solving Basic Equations 12  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Two Step Equation Word Problems Sample Problem 15  By will Mrs. Cabot was to receive five times as much as her son Henry. If Henry received $20,000 less than his mother, how much did each receive? 

Two Step Equation Word Problems Sample Problem 19  Two men whose wages differ by eight dollars receive both together $44 per hour. How much does each receive? 

Two Step Equation Word Problems Sample Problem 23  Three firms lost $118,000 by fire. The second firm lost $6000 less than the first and $20,000 more than the third. What was each firm's loss? 
Exponents
Evaluating Exponential Functions 


Title/Subject  Description  
Evaluating Exponential Functions Sample Problem Set 1  Plugandchug with the evaluation of Exponential Functions.  
Graphing Exponential Functions 

Title/Subject  Description  
Graphing Exponential Functions Problem Set  We now have graphing utilities to take the "chore" out of graphing. However, we should still be able to manually calculate an (x, y) ordered pair on the graph of our function. 

Exponents with Multiplication 

Title/Subject  Description  
Problem Set 1  Our rules of exponents combine with arithmetic to give us ways to simplify fractions with factors raised to powers with ease.  
Problem Set 2  Our rules of exponents combine with arithmetic to give us quick ways to simplify fractions with factors raised to powers.  
Exponents with Division 

Title/Subject  Description  
Problem Set 1  Both multiplication and division are operations within the division worksheet from MathAids.com.  
Problem Set 2  Whether multiplication or division, we employ the rules of exponents to simplify fractions with factors raised to powers.  
Exponents with Multiplication and Division 

Title/Subject  Description  
Crossing the Fraction Bar  To simplify a fraction with factors in the numerator and in the denominator, move a factor across the fraction bar and change the sign of the exponent.  
Fraction Bar Crossing  Multiplication and Division; Positive and Negative Exponents. Practice until these manipulations are easy and secondnature to you. 

Learn to Cross the Fraction Bar  Do not fret about whether we move factors with multiplication or division. Just move them, and get ready for the language of algebra. 

Powers of Products 

Title/Subject  Description  
Powers of Products 1  Monomials, as Products, raised to Powers.  
Powers of Products Practice Problems  Six problems with positive exponents help us understand some of the ways to simplify terms raised to powers.  
Powers of Quotients 

Title/Subject  Description  
Fractions to Powers  Quotients, in the form of fractions, are raised to powers.  
Quotients to Powers  Quotients to Powers, employing the Rules of Exponents.  
Powers of Products and Quotients 

Title/Subject  Description  
Exponents for Products and Quotients  Products and Quotients; Quotients and Products. They use the same rules of Exponents. 

Exponents for Products and Quotients 2  Products and Quotients; Quotients and Products. We practice working with the Rules of Exponents. 

Operations with Exponents 

Title/Subject  Description  
Operations with Exponents Problem Set 1  More practice with Exponents.  
Operations with Exponents Problem Set 2  To learn the language of math requires practice, like we do with these simplifcations of Factors and Exponents.  
Writing Numbers in Scientific Notation 

Title/Subject  Description  
Writing Numbers in Scientific Notation Problem Set  It is important to express values in Scientific Notation. We should also write numbers in Standard Form that are given to us in Scientific Notation. 

Operations with Scientific Notation 

Title/Subject  Description  
Operations with Scientific Notation Problem Set 1  Here we multiply values expressed in Scientific Notation. We have only Positive Powers in this video. 

Operations with Scientific Notation Problem Set 2  Here we multiply and divide values expressed in Scientific Notation. We have only Positive Powers in this video. 
General Topics
General Topics 


Title/Subject  Description  
Adding and Subtracting Rational Numbers 14010  A worksheet from MathAids.com to practice addition and subtraction of rational numbers, including negatives.  
AFBIA, Exercise 12  From A First Book in Algebra, Boyden, 1895. Learn the basics. 

AFBIA, Exercise 13  From A First Book in Algebra, Boyden, 1895. Learn the basics. 

AFBIA, Exercise 14  From A First Book in Algebra, Boyden, 1895. Learn the basics. 

AFBIA, Exercise 15  From A First Book in Algebra, Boyden, 1895. Learn the basics. 

AFBIA, Exercise 16  From A First Book in Algebra, Boyden, 1895. Learn the basics. 

AFBIA, Exercise 4  From A First Book in Algebra, Boyden, 1895. Learn the basics. 

AFBIA, Exercise 5  From A First Book in Algebra, Boyden, 1895. Learn the basics. 

Algebra Practice MS45  From Microsoft Education Labs, a practice worksheet for basic algebra.  
Algebra Practice MS47  From Microsoft Education Labs, a practice worksheet for basic algebra.  
Algebra Practice MS48  From Microsoft Education Labs, a practice worksheet for basic algebra.  
Algebra Translated 32  From MathAids.com, a worksheet to practice turning English into math. Go to MathAids.com and build your own math worksheets to practice. 

Algebra Translated 33  From MathAids.com, a worksheet to practice turning English into math. Go to MathAids.com and build your own math worksheets to practice. 

Basic Algebra Problem 010  An illustrative example: The sum of two numbers is 60, and the greater is four times the less. What are the numbers? 

Basic Algebra Problem 11  A man bought a horse and carriage for $500, paying three times as much for the carriage as for the horse. How much did each cost? 

Basic Algebra Problem 111  Graphing points in Cartesian (or rectangular) coordinates; a worksheet from MathAids.com  
Basic Algebra Problem 112  The idea of this worksheet from mathAids.com is that we can plot points to draw a shape.  
Basic Algebra Problem 113  This is a fairly involved set of points to plot in a worksheet from mathAids.com.  
Basic Algebra Problem 114  Plotting pints involves matching up sets of ordered pairs. Keep the xcoordinate and the ycoordinate straight, and it's a snap. 

Basic Algebra Problem 115  From MathAids.com we have a worksheet with square roots. Simplify the radicals. 

Basic Algebra Problem 116  This worksheet from mathAids.com involving radicals (square roots) is really a test of your mastery of basic facts of multiplication. If you know that 9 times 5 is 45, then âˆš45 = âˆš9 times âˆš5, or 3 times âˆš5. 

Basic Algebra Problem 117  Another worksheet for simplifying radicals. In each case we're looking for factors underneath the radical that are perfect squares. We "pull those factors out." 

Basic Algebra Problem 118  Look for factors in the radicand, underneath the square root sign; that's the name of this game.  
Basic Algebra Problem 119  These are facts in a worksheet from MathAids.com that you should know. We simplify, so learn learn these. Some things you just have to know. You should memorize a number of integers raised to powers 2, 3, and even 4 and 5. 

Basic Algebra Problem 12  For 72 cents Martha bought some needles and thread, paying eight times as much for the thread as for the needles. How much did she pay for each? 

Basic Algebra Problem 120  Solve the exponents. In this worksheet we're really not solving for anything, we are simplifying. 

Basic Algebra Problem 121  From our good friends at MathAids.com is a sheet for function tables. We generate yvalues for a given simple function. The xvalues are inputs to the function. 

Basic Algebra Problem 122  Given xvalues, we figure out the yvalues for these linear relations, or functions. The lines on this particular worksheet each pass through the origin (0, 0). 

Basic Algebra Problem 123  From MathAids: They provide the xvalue. We want to come up with the yvalue based on the linear relationship given for each function. 

Basic Algebra Problem 124  From our good friends at MathAids.com, we generate ordered pairs for xy tables, for linear functions.  
Basic Algebra Problem 125  Complete the table, from MathAids.com, for yvalues for a given function and set of xvalues.  
Basic Algebra Problem 126  Once again, we're given the xcoordinate for points on a line, and we generate the yvalue, or the output of the function for each x input.  
Basic Algebra Problem 127  Complete the function tables in a worksheet from MathAids.com.  
Basic Algebra Problem 128  This worksheet from mathAids.com has "In and Out Boxes" that are another form of xy tables for functions.  
Basic Algebra Problem 129  More InandOutBoxes. We just follow what the functions tell us to do, from MathAids. 

Basic Algebra Problem 13  An illustrative example: What number added to twice itself and 40 more will make a sum equal to eight times the number?  
Basic Algebra Problem 130  InandOut Boxes, from MathAids.com. These are a snap if you know basic facts of arithmetic. 

Basic Algebra Problem 131  We're talking about functions with these InandOut Boxes. Think "inputs" and "outputs." Y is a function of x. 

Basic Algebra Problem 132  We fill in empty boxes according to the rules given for each function. These are InandOut Boxes for inputs and outputs, x and y, respectively. 

Basic Algebra Problem 133  Just follow the recipe for these functions in this worksheet from MathAids.com, for inputs and outputs, for the independent variable and the dependent variable.  
Basic Algebra Problem 134  InandOut Boxes have us multiply by an integer to generate the outputs to the function.  
Basic Algebra Problem 135  Multiply or divide in this worksheet from MathAids.com. Our InandOut Boxes are function tables, basically. 

Basic Algebra Problem 14  James is 3 years older than William, and twice James's age is equal to three times William's age. What is the age of each? 

Basic Algebra Problem 15  Roger is onefourth as old as his father, and the sum of their ages is 70 years. How old is each? 

Basic Algebra Problem 30  An illustrative example: If the difference between two numbers is 48, and one number is five times the other, what are the numbers?  
Basic Algebra Problem 304  This work in Advanced Algebra is appropriate for good students in Basic Algebra.  
Basic Algebra Problem 305  This problem, typically encountered in Advanced Algebra, is appropriate for quality students in Basic Algebra. Ten problems; I work the first five. 

Basic Algebra Problem 306  These problems from Advanced Algebra can be done by advanced students in Basic Algebra. Ten problems; I work four and leave six for you to work. 

Basic Algebra Problem 33  James gathered 12 quarts of nuts more than Henry gathered. How many did each gather if James gathered three times as many as Henry? 

Basic Algebra Problem 330  An advanced Algebra problem appropriate for a course in Basic Algebra.  
Basic Algebra Problem 36  Mr. A is 48 years older than his son, but he is only three times as old. How old is each? 

Basic Algebra Problem 40  A man bought a hat, a pair of boots, and a necktie for $$7.50; the hat cost four times as much as the necktie, and the boots cost five times as much as the necktie. What was the cost of each? 

Basic Algebra Problem 46  There are 120 pigeons in three flocks. In the second there are three times as many as in the first, and in the third as many as in the first and second combined. How many pigeons in each flock? 

Basic Algebra Problem 47  Three men, A, B, and C, earned $110; A earned four times as much as B, and C as much as both A and B. How much did each earn? 

Basic Algebra Problem 48  A farmer bought a horse, a cow, and a calf for $72; the cow cost twice as much as the calf, and the horse three times as much as the cow. What was the cost of each? 

Basic Algebra Problem 50  A grocer sold one pound of tea and two pounds of coffee for $1.50, and the price of the tea per pound was three times that of the coffee. What was the price of each? 

Basic Algebra Problem 52  By will Mrs. Cabot was to receive five times as much as her son Henry. If Henry received $20,000 less than his mother, how much did each receive? 

Basic Algebra Problem 53  An illustrative example: Divide the number 126 into two parts such that one part is 8 more than the other.  
Basic Algebra Problem 55  At an election in which 1079 votes were cast the successful candidate had a majority of 95. How many votes did each of the two candidates receive? 

Basic Algebra Problem 56  John and Henry together have 143 marbles. If I should give Henry 15 more, he would have just as many as John. How many has each? 

Basic Algebra Problem 57  Two men whose wages differ by eight dollars receive both together $44 per hour. How much does each receive? 

Basic Algebra Problem 58  Divide 62 into three parts such that the first part is 4 more than the second, and the third 7 more than the second.  
Basic Algebra Problem 59  A man had 95 sheep in three flocks. In the first flock there were 23 more than in the second, and in the third flock 12 less than in the second. How many sheep in each flock? 

Basic Algebra Problem 60  A man owns three farms. In the first there are 5 acres more than in the second and 7 acres less than in the third. If there are 53 acres in all the farms together, how many acres are there in each farm? 

Basic Algebra Problem 61  Three firms lost $118,000 by fire. The second firm lost $6000 less than the first and $20,000 more than the third. What was each firm's loss? 

Basic Algebra Problem 62  In an orchard containing 33 trees the number of pear trees is 5 more than three times the number of apple trees. How many are there of each kind? 

Basic Algebra Problem 64  To the double of a number I add 17 and obtain as a result 147. What is the number? Also: To four times a number I add 23 and obtain 95. Also: From three times a number I take 25 and obtain 47. Also: Find a number which being multiplied by 5 and having 14 added to the product will equal 69. 

Basic Algebra Problem 66  I bought some tea and coffee for $10.39. If I paid for the tea 61 cents more than five times as much as for the coffee, how much did I pay for each? 

Basic Algebra Problem 67  Two houses together contain 48 rooms. If the second house has 3 more than twice as many rooms as the first, how many rooms has each house? 

Basic Algebra Problem 68  Mr. Ames builds three houses. The first cost $2000 more than the second, and the third twice as much as the first. If they all together cost $18,000, what was the cost of each house? 

Basic Algebra Problem 70  George bought an equal number of apples, oranges, and bananas for $1.08; each apple cost 2 cents, each orange 4 cents, and each banana 3 cents. How many of each did he buy? 

Basic Algebra Problem 72  A man bought 3 lamps and 2 vases for $6. If a vase cost 50 cents less than 2 lamps, what was the price of each? 

Basic Algebra Problem 73  Johnson and May enter into a partnership in which Johnson's interest is four times as great as May's. Johnson's profit was $4500 more than May's profit. What was the profit of each? 

Basic Algebra Problem 74  Divide 71 into three parts so that the second part shall be 5 more than four times the first part, and the third part three times the second.  
Basic Algebra Problem 75  I bought a certain number of barrels of apples and three times as many boxes of oranges for $33. I paid $2 a barrel for the apples, and $3 a box for the oranges. How many of each did I buy? 

Basic Algebra Problem 76  Divide the number 288 into three parts, so that the third part shall be twice the second, and the second five times the first.  
Basic Algebra Problem 77  If John's age be multiplied by 5, and if 24 be added to the product, the sum will be seven times his age. What is his age? 

Basic Algebra Problem 78  A man, being asked how many sheep he had, said, "If you will give me 24 more than six times what I have now, I shall have ten times my present number." How many had he?  
Basic Algebra Problem 79  Four dozen oranges cost as much as 7 dozen apples, and a dozen oranges cost 15 cents more than a dozen apples. What is the price of each? 

Basic Algebra Problem 80  A farmer pays just as much for 4 horses as he does for 6 cows. If a cow costs 15 dollars less than a horse, what is the cost of each? 

Basic Algebra Problem 81  Roger is onefourth as old as his father, and the sum of their ages is 70 years. How old is each? 

Basic Algebra Problem 82  Jane is onefifth as old as Mary, and the difference of their ages is 12 years. How old is each? 

Basic Algebra Problem 83  Two men own a third and twofifths of a mill respectively. If their part of the property is worth $22,000, what is the value of the mill? 

Basic Algebra Problem 85  In three pastures there are 42 cows. In the second there are twice as many as in the first, and in the third there are onehalf as many as in the first. how many cows are there in each pasture? 

Basic Algebra Problem 87  What number increased by threesevenths of itself will amount to 8640?  
Basic Algebra Problem 88  There are three numbers whose sum is 90; the second is equal to onehalf of the first, and the third is equal to the second plus three times the first. What are the numbers? 

Basic Algebra Problem 89  A grocer sold 62 pounds of tea, coffee, and cocoa. Of tea he sold 2 pounds more than of coffee, and of cocoa 4 pounds more than of tea. How many pounds of each did he sell? 

Basic Algebra Problem 90  John has oneninth as much money as Peter, but if his father should give him 72 cents, he would have just the same as Peter. How much money has each boy? 

Basic Algebra Problem 91  Two boys picked 26 boxes of strawberries. If John picked fiveeighths as many as Henry, how many boxes did each pick? 

Basic Algebra Problem 94  In a school containing 420 pupils, there are threefourths as many boys as girls. How many are there of each? 

Basic Algebra Problem 95  One man carried off threesevenths of a pile of soil, another man fourninths of the pile. In all they took 110 cubic yards of earth. How large was the pile at first? 

Basic Algebra Problem 96  Matthew had three times as many stamps as Herman, but after he had lost 70, and Herman had bought 90, they put what they had together and found that they had 540 stamps. How many had each at first? 

Basic Word Problems 11  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
Basic Word Problems 12  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
Basic Word Problems 13  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
Basic Word Problems 14  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
Basic Word Problems 15  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
Basic Word Problems 16  Basic word problems in basic algebra are arithmetic problems with an occasional variable thrown into it.  
Connecting Nodes  A geometric lesson appropriate for Basic Algebra.  
Essentials of basic algebra.  A very basic lesson in terms with a single variable. We solve Solve 3x + 5x = 72. 

Exam (lesson) on Properties of Arithmetic/Algebra  This little exam, a quiz really, uses a worksheet from MathAids.com to illustrate the concepts of Commutative Properties, Associative Properties, Distributive Properties, and Identity Properties. The final 15 out of 25 questions comprise a quiz. 

Find the Missing Angle 14013  In a worksheet for quadrilaterals from mathAids.com, find the measure of the missing angle given three of the interior angles of a foursided polygon.  
Find the Missing Angle 14014  Given three interior angle measures in quadrilaterals labeled by vertices, find the measure of the missing interior angle.  
Inequality in One Variable with Absolute Value  This Advanced Algebra problem is pretty basic, and is appropriate toward the end of a Basic Algebra course.  
Know Your Roots  Appropriate for both Arithmetic and Basic Algebra, you need to learn simple positive roots of squares of integers. Yes, you have to learn them. 

Know Your Roots and PRACTICE  In both Arithmetic and Basic Algebra, LEARN YOUR ROOTS.  
Linear Equations in 1 Variable  These problems should be readily solved by anyone with a familiarity with algebra. these are very basic equations. 

Linear Equations in One Variable  To learn algebra these problems of distribution need to be mastered.  
PEMDAS, Order of Operations 14004  You have to get a feel for order of operations to have an easy time with algebra. These basics need to be understood by anyone doing math beyond arithmetic. 

PEMDAS, Order of Operations 14005  Order of Operations must be understood to solve algebraic expressions. PEMDAS is a familiar acronym to most algebra students. 

Powers and Roots  Six little problems help us to understand roots and exponents.  
Quadrilaterals and Polygons  Identify the Type for each Quadrilateral with a worksheet from MathAids.com.  
Sets of Real Numbers  Real Numbers can be categorized into various subsets: rational, irrational, integers, positive, negative, etc.  
Simplify Algebraic Fractions  Twelve problems, six of them "worked." We factor out from numerator and denominator common factors, most often linear factors. This is also a Problem Set in Advanced Algebra. 

Simplifying Algebraic Expressions 14006  We learn to simplify algebraic expressions with practice.  
Simplifying Algebraic Expressions 14007  We learn to simplify algebraic expressions with practice.  
Solve Linear Eqns. Problem Set 01  We practice basic equations in x. All of these equations are linear, that is, x is to the firstpower only. 

Solve Linear Eqns. Problem Set 02  We practice the very basics of the language of algebra.  
Solve Linear Eqns. Problem Set 03  Practice with some very basic algebraic expressions.  
Solve Linear Eqns. Problem Set 04  Practice with simple and basic expressions in x.  
Solve Linear Eqns. Problem Set 05  Practice with basic expressions in x that involve fractions.  
Solve Linear Eqns. Problem Set 06  All of our xterms are to the first power. This makes these equations linear. Solve, please. 

Solve Linear Eqns. Problem Set 07  Problems in early algebra. These are basic and straightforward. 

Solve Linear Eqns. Problem Set 08  Basic linear equations here involve fractions and several different techniques. Solve, please. 

Solve Linear Eqns. Problem Set 11  We practice distributing over binomials, combining like terms, and solving for x. So practice solving these simple expressions for x. 

Solve Two Linear Eqns 263  We solve two linear equations and examine the graph of their intersection at desmos.com.  
Solve Two Linear Eqns 264  We solve for the simultaneous solution to two linear equations. We find where the lines intersect. 

Solving Basic Equations 01  Simple and straightforward algebraic expressions with a single variable. This is a great place to begin working algebra problems. 

Solving Basic Equations 02  We compare the distribution of a factor over a binomial with substitution within the binomial to solve simple equations.  
Solving Basic Equations 03  We soon discover that understanding (knowing) the basic facts of multiplication helps us greatly in soling algebraic equations. We also treat both sides of an equation identically, to simplify our lives. 

Solving Basic Equations 04  Again, I'll do the oddnumbered problems. When things are obvious, we recommend that you simply write the answer. Or, when obvious, simplify along the way. 

Solving Basic Equations 05  We cannot overemphasize the need to know basic facts of arithmetic, especially the multiplication table. Knowing facts makes life so much easier. 

Solving Basic Equations 06  Sixteen problems. I'll do the odds. Fractions are easy if you understand arithmetic and basic facts of addition and multiplication. 

Solving Basic Equations 07  I'll do the odds. More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Solving Basic Equations 08  Combine like terms and practice arithmetic as we solve simple equations in one variable.  
Solving Basic Equations 09  Combine like terms. Treat both sides of the equations identically to simplify the equations in one variable. Practice with fractions, too. 

Solving Basic Equations 10  Subtract or add the same quantity to both sides of an equation. It gets easy with practice. Knowing arithmetic makes it easy. Sometimes we show more than one way to solve. 

Solving Basic Equations 11  When solutions are obvious, we recommend you simply write the answer. We practice cancelling factors "top and bottom" in fractions. 

Solving Basic Equations 12  Combine like terms. Cancel factors top and bottom. Distribute over binomials. See different ways to solve simple equations in one variable. 

Solving Basic Equations 13  A comprehensive review of basic problems. Fifty simple problems. I'll do the odds. 

Solving Basic Linear Equations 14  Solve linear pairs of equations in two variables. We begin with easy examples. The solutions are simultaneous. 

Solving Basic Linear Equations 15  Elimination of a variable is a good technique to solve many pairs of linear equations in two variables. Generally we either add or subtract equations to eliminate one of the variables. 

Solving Basic Linear Equations 16  Don't let fractions get in the way of solving equations. Just use what you have already learned. 

Solving Basic Linear Equations 17  We give you a break with fewer fractions than the previous problem set. Relax and apply what you already know. 

Solving Basic Linear Equations 18  Eliminate a variable. Distribute. Rewrite equations with substitutions. Solve. 

Solving Basic Linear Equations 19  Find the values that make both statements true. There is (generally) a unique solution to a pair of linear equations. It is a simultaneous solution. 

Solving Basic Linear Equations 20  Eliminate a variable. Solve for the unknowns. We may also isolate a variable and use the Substitution Method. 

Solving Basic Linear Equations 21  Plug back in and rewrite the other equation as we solve linear equations. By now your techniques should be more comfortable. 

Solving Basic Linear Equations 22  Multiply equations by different factors to get opposite coefficients on the same variable. Then eliminate a variable. Or substitute. Solve for the other. Then plug back in and rewrite. 

Solving Basic Linear Equations 23  Sometimes we substitute. Sometimes we eliminate a variable. Solve for one and rewrite the other equation, then solve for the other variable. 

Solving Basic Linear Equations 24  Watch your minus signs as we add equations to one another or subtract one equation from another.  
Solving Basic Linear Equations 25  Multiply an equation through by a factor to eliminate a variable. Practice makes this a very easy proposition. Don't let the fractions throw you. Practice. 

Solving Basic Linear Equations 26  Twentyfive problems. I'll do them all. BUT YOU SHOULD DO THEM FIRST. 

Solving Basic Quadratic Equations 27  A problem set in factoring secondorder polynomials in one variable, i.e. quadratics. 

Solving Basic Quadratic Equations 28  Factoring quadratics of the form axÂ²  bx +c = 0. You will see the pattern. Remember, when we end up with the Quadratic Formula we want the equation in the form axÂ² + bx +c = 0. 

Solving Basic Quadratic Equations 29  While this is still Basic Algebra, it begins to lead us toward Advanced Algebra. We factor secondorder polynomials into linear factors. 

Solving Basic Quadratic Equations 30  We're factoring more quadratics. Coefficients with many factors give us reason to scratch our heads just a little. 

Solving Basic Quadratic Equations 31  Factoring secondorder polynomials in one variable (quadratics) into linear factors, or binomials. We employ a variety of techniques. 

Solving Basic Quadratic Equations 32  More factoring of quadratics. Practice and knowing facts of arithmetic are key. We look briefly at a graph from Wolfram Alpha. 

Solving Basic Quadratic Equations 33  Not every quadratic equation factors into neat binomials or linear factors. In such cases we use the Quadratic Formula. 

Solving Basic Quadratic Equations 34  Factor, if possible. If the quadratic will not factor, use the Quadratic Formula. Build experience to see factorizations when they're possible. 

Solving Basic Quadratic Equations 35  We now emphasize the Quadratic Formula, which always serves to solve for the roots of an equation of the form axÂ² + bx + c = 0.  
Solving Basic Quadratic Equations 36  The Quadratic Formula works every time on an equation of the form axÂ² + bx + c = 0.  
Solving Basic Quadratic Equations 37  Factor (if possible) or use the Quadratic Formula. We're keeping things real at this point. 

Solving Basic Quadratic Equations 38  We introduce the complex solution when our quadratic has a negative discriminant. If this is beyond the scope of your work in Basic Algebra, that's just fine. Don't worry about it. 

Solving Basic Quadratic Equations 39  Twentyfive problems, all solved for you, for quadratics of all kinds (mostly basic). You should work them before watching the video. 

Translate Algebraic Expressions  moderate  From MathAids.com, a worksheet to translate algebraic expressions with two real values and one variable.  
Translate Algebraic Expressions 14001  From MathAids.com, a basic worksheet with ten problems to translate English into math. This is basic algebra. 
Inequalities
Graphing Single Variable 


Title/Subject  Description  
Graphing Single Variable Inequalities Sample Problem 1  There are two types of problems we work on this problem set. We graph single variable inequalities in some problems. In the others we identify the inequality from the graph. Our inequalities include less than (<), less than or equal to (<e;), greater than (>), and greater than or equal to (>e;). 

Graphing Single Variable Inequalities Sample Problem 2  Graphing Inequalities in One Variable is an easy and straightforward task.  
One Step Inequalities by Adding and Subtracting 

Title/Subject  Description  
One Step Inequalities by Adding and Subtracting Problem Set 1  We solve onestep inequalities with each of the four basic operations of arithmetic. Then we graph the Solution Set on the Real Number Line. 

One Step Inequalities by Multiplying and Dividing 

Title/Subject  Description  
One Step Inequalities by Multiplying and Dividing Problem Set 1  Onestep Inequalities are a great place to begin in earnest your study of inequalities.  
Two Step Inequalities 

Title/Subject  Description  
Two Step Inequalities Problem Set 1  Twostep problems here, where we solve for the variable (or unknown, or letter) and express the Solution Set. Then we graph the Solution Set on the Real Number Line. 

Multiple Step Inequalities 

Title/Subject  Description  
Multiple Step Inequalities Problem Set 1  We use all four basic arithmetic operations to find the Solution Set for these inequalities. 
Inequalities
Graphing Single Variable Inequalities 


Title/Subject  Description  
Graphing Single Variable Inequalities Sample Problem 1  There are two types of problems we work on this problem set. We graph single variable inequalities in some problems. In the others we identify the inequality from the graph. Our inequalities include less than ( < ), less than or equal to ( ≤ ), greater than ( > ), and greater than or equal to ( ≥ ). 

Graphing Single Variable Inequalities Sample Problem 2  Graphing Inequalities in One Variable is an easy and straightforward task.  
One Step Inequalitites by Adding and Subtracting 

Title/Subject  Description  
One Step Inequalities by Adding and Subtracting Problem Set 1  Onestep Inequalities are a great place to begin in earnest your study of inequalities.  
One Step Inequalities by Multiplying and Dividing 

Title/Subject  Description  
One Step Inequalities by Multiplying and Dividing Problem Set 1  We solve these basic inequalities with either multiplication or division. Then we graph the Solution Set on the Real Number Line. 

One Step Inequalities by Adding, Subtracting, Multiplying and Dividing 

Title/Subject  Description  
One Step Inequalities by Adding, Subtracting, Multiplying and Dividing Problem Set 1  We solve onestep inequalities with each of the four basic operations of arithmetic. Then we graph the Solution Set on the Real Number Line. 

Two Step Inequalities 

Title/Subject  Description  
Two Step Inequalities Problem Set 1  Twostep problems here, where we solve for the variable (or unknown, or letter) and express the Solution Set. Then we graph the Solution Set on the Real Number Line. 

Multiple Step Inequalities 

Title/Subject  Description  
Multiple Step Inequalities Problem Set 1  We use all four basic arithmetic operations to find the Solution Set for these inequalities.  
Compound Inequalities 

Title/Subject  Description  
Compound Inequalities Problem Set 1  The conjunctions OR and AND make all the difference in the relationship between our sets. The "name of the game" is to find all the values that satisfy the original inequalities, either both (AND) or either (OR). 

Absolute Value Inequalities 

Title/Subject  Description  
Absolute Value Inequalities Problem Set 1  With Absolute Value we get a compound situation. Two sets will either overlap (intersect) or be combined (a union). 
Linear Equations & Inequalities
Finding Slope from a Graphed Line 


Title/Subject  Description  
Finding Slope from a Graphed Line Problem Set 1  These problems require us to identify the slope of a Graphed Line. Download the worksheet to work these problems with Mr. X. 

Finding Slope from a Pair of Points 

Title/Subject  Description  
Finding Slope from a Pair of Points Problem Set  It is easy to determine the slope of a line given two points (two ordered pairs) on that line. We also like to call slope the ratio of "rise over run." 

Finding Slope and Yintercept from a Linear Equation 

Title/Subject  Description  
Finding Slope and Yintercept from a Linear Equation Problem Set 1  Here we read the "m" from y = mx + b. We might call this Problem Set a Slam Dunk. 

Finding Slope and Yintercept from a Linear Equation Problem Set 2  Each of the equations in this video are already in the SlopeIntercept Form for the Equation of Line. We just read the values of "m" and "b." 

Finding Slope and Yintercept from a Linear Equation Problem Set 3  We rearrange the Standard Form for Equations of Lines to the familiar y = mx + b.  
Graphing Lines in SlopeIntercept Form 

Title/Subject  Description  
Graphing Lines in SlopeIntercept Form Problem Set 1  Given the Equation of a Line in SlopeIntercept form, we graph the line (actually, we graph a line segment that is on that line) on a 10x10 grid.  
Graphing Lines in SlopeIntercept Form Problem Set 2  We sketch line segments on a 10x10 grid using the given slopes and yintercepts.  
Graphing Lines in SlopeIntercept Form Problem Set 3  We sketch line segments on a 10x10 grid using the given slopes and yintercepts.  
Graphing Lines Given YIntercept and an Ordered Pair 

Title/Subject  Description  
Graphing Lines given YIntercept and an Ordered Pair Problem Set 1  We graph the line (segment) that contains both given points. The yintercept has an xcoordinate of zero. 

Graphing Lines given YIntercept and an Ordered Pair Problem Set 2  Two points determine a line. Here we also get the equation of the line in slopeintercept form, as y = mx + b. 

Graphing Lines Given Two Ordered Pairs 

Title/Subject  Description  
Graphing Lines Given Two Ordered Pairs Sample Problem  Given two Ordered Pairs, we can easily write the Equation of a Line. The task is made easier when the yintercept is already given, as well. 

Graphing Lines in Standard Form 

Title/Subject  Description  
Graphing Lines in Standard Form Problem Set 1  Given the Equation of a Line in Standard Form, we graph a portion of that line on a 10x10 grid.  
Graphing Lines in Standard Form Problem Set 2  Given the Equation of a Line in Standard Form, we graph a portion of that line on a 10x10 grid.  
Working with Linear Equations 

Title/Subject  Description  
Working with Linear Equations Problem Set 1  We solve a variety of problems involving the SlopeIntercept Form for the Equation of a Line.  
Writing Linear Equations 

Title/Subject  Description  
Writing Linear Equations Problem Set 1  We write the Equation of a Line in SlopeIntercept Form from a Graph of the Line.  
Graphing Linear Inequalitites 

Title/Subject  Description  
Graphing Linear Inequalities Problem Set 1  When we graph Linear Inequalities we shade half of the Cartesian Plane.  
Graphing Absolute Values 

Title/Subject  Description  
Graphing Absolute Values Problem Set  Graphing Absolute Value functions is good practice for Basic Algebra. 
Linear Functions
Finding Slope from a Graphed Line 


Title/Subject  Description  
Finding Slope from a Graphed Line Problem Set 1  These problems require us to identify the slope of a Graphed Line. Download the worksheet to work these problems with Mr. X. 

Finding Slope from a Pair of Points 

Title/Subject  Description  
Finding Slope from a Pair of Points Problem Set  It is easy to determine the slope of a line given two points (two ordered pairs) on that line. We also like to call slope the ratio of "rise over run." 

Finding Slope and YIntercept from a Linear Equation 

Title/Subject  Description  
Finding Slope and Yintercept from a Linear Equation Problem Set 1  Here we read the "m" from y = mx + b. We might call this Problem Set a Slam Dunk. 

Finding Slope and Yintercept from a Linear Equation Problem Set 2  Each of the equations in this video are already in the SlopeIntercept Form for the Equation of Line. We just read the values of "m" and "b." 

Finding Slope and Yintercept from a Linear Equation Problem Set 3  We rearrange the Standard Form for Equations of Lines to the familiar y = mx + b.  
Graphing Lines in SlopeIntercept Form 

Title/Subject  Description  
Graphing Lines in SlopeIntercept Form Problem Set 1  Given the Equation of a Line in SlopeIntercept form, we graph the line (actually, we graph a line segment that is on that line) on a 10x10 grid.  
Graphing Lines in SlopeIntercept Form Problem Set 2  We sketch line segments on a 10x10 grid using the given slopes and yintercepts.  
Graphing Lines in SlopeIntercept Form Problem Set 3  We sketch line segments on a 10x10 grid using the given slopes and yintercepts.  
Graphing Lines in Standard Form 

Title/Subject  Description  
Graphing Lines in Standard Form Problem Set 1  Given the Equation of a Line in Standard Form, we graph a portion of that line on a 10x10 grid.  
Graphing Lines in Standard Form Problem Set 2  Given the Equation of a Line in Standard Form, we graph a portion of that line on a 10x10 grid.  
Working with Linear Equations 

Title/Subject  Description  
Working with Linear Equations Problem Set 1  We solve a variety of problems involving the SlopeIntercept Form for the Equation of a Line.  
Writing Linear Equations 

Title/Subject  Description  
Writing Linear Equations Problem Set 1  We write the Equation of a Line in SlopeIntercept Form from a Graph of the Line.  
Graphing Linear Inequalities 

Title/Subject  Description  
Graphing Linear Inequalities Problem Set 1  When we graph Linear Inequalities we shade half of the Cartesian Plane. 
Monomial and Polynomials
Identifying the Type of Monomials and Polynomials 


Title/Subject  Description  
Types of Monomials and Polynomials Problem Set 1  Terms within a polynomial are separated by "plus" or "minus" signs.  
Identifying the Degree of Monomials and Polynomials 

Title/Subject  Description  
Identifying the Degree of Monomials and Polynomials Problem Set 1  We identify the degree of a polynomial by identifying the highestdegree term.  
Identifying the Degree of Monomials and Polynomials Problem Set 2  To identify the degree of a polynomial, we find the term with the highest degree. One technique is to add the exponents on the variables within each term of the polynomial. 

Naming of Monomials and Polynomials 

Title/Subject  Description  
Naming Monomials and Polynomials Problem Set 1  We may find the highestdegree term and assign that degree to the polynomial.  
Adding and Subtracting Monomials and Polynomials 

Title/Subject  Description  
Adding and Subtracting Monomials and Polynomials Problem Set 1  Combine Like Terms. Here we add or subtract polynomials with "like terms." Combine those terms raised to like powers with addition or subtraction of coefficients. 

Adding and Subtracting Monomials and Polynomials Problem Set 2  Basic skills in Algebra include the ability to Combine Like Terms. When we add or subtract polynomials we do this to simplify our lives. Really, this makes our lives simpler. 

Multiplying Polynomials 

Title/Subject  Description  
Multiplying Polynomials Problem Set 1  We start learning the multiplication of polynomials with simple examples. You must know your basic facts of multiplication. You must know your Times Table. 

Multiplying Polynomials Problem Set 2  As we multiply more terms and more variables, the rules stay the same. When we multiply polynomials, the leading term in front of the parentheses multiplies each term within the parentheses. 

Multiplying Polynomials Problem Set 3  As we multiply more terms and more variables, the rules stay the same. When we multiply polynomials, the leading term in front of the parentheses multiplies each term within the parentheses. We soon get squared terms and cubed terms. 

Multiplying Polynomials Problem Set 4  The multiplication of polynomials will soon become secondnature to you. But you have to practice. And you have to know your facts from the Times Table. 

Multiplying Special Case 

Title/Subject  Description  
Multiplying Special Case Problem Set 1  We take a good look at the Difference of Two Squares. This is a pattern you should recognize as we learn to multiply polynomials. 

Multiplying Special Case Problem Set 2  The pattern of the Factorization of the Difference of Two Squares is easy to recognize. If you know your squares (of small integers) you will find this very, very easy. 

Multiplying Special Case Problem Set 3  It's the first term squared plus twice the product of the two terms plus the last term squared. This is how we Square a Binomial. 

Dividing Polynomials 

Title/Subject  Description  
Dividing Polynomials with Factoring Practice Problems 1  The polynomials in these problems will share factors. We factor out from numerator and denominator common factors, most often linear factors. Make sure you can solve these problems before working with the more advanced problems available on this section. 

Dividing Polynomials with Long Division 

Title/Subject  Description  
Dividing Polynomials with Long Division Lesson & Problem Set 1  The long division of polynomials is a skill to be developed with practice. If you rely on a machine to give you the quotients, you will not learn it. 

Dividing Polynomials with Long Division Solved Problems  Division of polynomials can be done with a process that looks just like "long division."  
Factoring Quadratic 

Title/Subject  Description  
Factoring Quadratic Polynomials Problem Set 1  We factor quadratics. Some problems will have the first coefficient be greater than one. Some of these polynomials will not be factorable. 

Factoring Special Case 

Title/Subject  Description  
Factoring Special Case Monomial and Polynomials Problem Set 1  Here we practice factoring statements that might include the Difference of Two Squares. You should know that a^{2}  b^{2} = (a + b)(a  b). 

Factoring Special Case Monomial and Polynomials Problem Set 2  Perfect Squares of Binomials and the Difference of Two Squares appear on the worksheet. Practice these techniques if you have more math courses in your future. 

Factoring Special Case Monomial and Polynomials Problem Set 3  A problem set in factorization with grouping and statements with four terms. If you have higher math courses in your future, you should practice these and build your skills. 

Factoring Special Case Monomial and Polynomials Problem Set 4  We factor expressions with practice. So practice. And learn the language of Algebra. 

Factoring by Grouping 

Title/Subject  Description  
Factoring by Grouping Problem Set 1  For this worksheet you can learn an algorithm, or recipe. We can factor by grouping. If the statement will not factor, write "nonfactorable" or N.C.D. 
Monomials and Polynomials
Identifying the Type of Monomials and Polynomials 


Title/Subject  Description  
Types of Monomials and Polynomials Problem Set 1  Terms within a polynomial are separated by "plus" or "minus" signs.  
Identifying the Degree of Monomials and Polynomials 

Title/Subject  Description  
Identifying the Degree of Monomials and Polynomials Problem Set 1  We identify the degree of a polynomial by identifying the highestdegree term.  
Identifying the Degree of Monomials and Polynomials Problem Set 2  To identify the degree of a polynomial, we find the term with the highest degree. One technique is to add the exponents on the variables within each term of the polynomial. 

Adding and Subtracting Monomials and Polynomials 

Title/Subject  Description  
Adding and Subtracting Monomials and Polynomials Problem Set 1  Combine Like Terms. Here we add or subtract polynomials with "like terms." Combine those terms raised to like powers with addition or subtraction of coefficients. 

Adding and Subtracting Monomials and Polynomials Problem Set 2  Basic skills in Algebra include the ability to Combine Like Terms. When we add or subtract polynomials we do this to simplify our lives. Really, this makes our lives simpler. 

Multiplying Monomials and Polynomials 

Title/Subject  Description  
Multiplying Polynomials Problem Set 1  We start learning the multiplication of polynomials with simple examples. You must know your basic facts of multiplication. You must know your Times Table. 

Multiplying Polynomials Problem Set 2  As we multiply more terms and more variables, the rules stay the same. When we multiply polynomials, the leading term in front of the parentheses multiplies each term within the parentheses. 

Multiplying Polynomials Problem Set 3  As we multiply more terms and more variables, the rules stay the same. When we multiply polynomials, the leading term in front of the parentheses multiplies each term within the parentheses. We soon get squared terms and cubed terms. 

Multiplying Polynomials Problem Set 4  The multiplication of polynomials will soon become secondnature to you. But you have to practice. And you have to know your facts from the Times Table. 

Multiplying Binomials, Monomials, and Polynomials 

Title/Subject  Description  
Multiplying Polynomials Problem Set 1  We start learning the multiplication of polynomials with simple examples. You must know your basic facts of multiplication. You must know your Times Table. 

Multiplying Polynomials Problem Set 2  As we multiply more terms and more variables, the rules stay the same. When we multiply polynomials, the leading term in front of the parentheses multiplies each term within the parentheses. 

Multiplying Polynomials Problem Set 3  As we multiply more terms and more variables, the rules stay the same. When we multiply polynomials, the leading term in front of the parentheses multiplies each term within the parentheses. We soon get squared terms and cubed terms. 

Multiplying Polynomials Problem Set 4  The multiplication of polynomials will soon become secondnature to you. But you have to practice. And you have to know your facts from the Times Table. 
Quadratic Function
Graphing Quadratic Functions 


Title/Subject  Description  
Graphing Quadratic Functions Problem Set 1  Try not to rely entirely on machines to do your thinking for you. Some graphing can and should be done by hand. So, practice, and learn the language of mathematics. 

Graphing Quadratic Inequalities 

Title/Subject  Description  
Graphing Quadratic Inequalities Sample Problem  Quadratics graph to Parabolas. Quadratic Inequalities ask us to shade the region either above or below the Parabola. 

Completing the Square 

Title/Subject  Description  
Completing the Square Problem Set  We don't really solve anything here. We simply reinforce one of the steps in Completing the Square to solve a Quadratic. 

Completing the Square Problem Set 2  Completing the Square is one of many techniques for solving Quadratic Equations. To master the technique, all you have to do is practice, and learn the language of mathematics. 

Solving Quadratic Equations By Taking Square Roots 

Title/Subject  Description  
Solving Quadratic Equations  A Comprehensive Review  25 problems that can be solved using different techniques. Can you solve these problems before viewing the video? 

Solving Quadratic Equations By Factoring 

Title/Subject  Description  
Solving Quadratic Equations by Factoring Problem Set 1  A problem set in factoring secondorder polynomials in one variable, i.e. quadratics. 

Solving Quadratic Equations by Factoring Problem Set 2  Factoring quadratics of the form ax²  bx +c = 0. You will see the pattern. Remember, when we end up with the Quadratic Formula we want the equation in the form a² + bx +c = 0. 

Solving Quadratic Equations by Factoring Problem Set 3  We factor secondorder polynomials into linear factors in these problems.  
Solving Quadratic Equations by Factoring Problem Set 4  We're factoring more quadratics. Coefficients with many factors add complexity to the problems. 

Solving Quadratic Equations by Factoring Problem Set 5  Factoring secondorder polynomials in one variable (quadratics) into linear factors, or binomials. We employ a variety of techniques. 

Solving Quadratic Equations by Factoring Problem Set 6  More factoring of quadratics. Practice and knowing facts of arithmetic are key. 

Solving Quadratic Equations  A Comprehensive Review  25 problems that can be solved using different techniques. Can you solve these problems before viewing the video? 

Solving Quadratic Equations with the Quadratic Formula 

Title/Subject  Description  
Solving Quadratic Equations with the Quadratic Formula Problem Set 1  Not every quadratic equation factors into neat binomials or linear factors. In such cases we use the Quadratic Formula. 

Solving Quadratic Equations with the Quadratic Formula Problem Set 2  Factor, if possible. If the quadratic will not factor, use the Quadratic Formula. Build experience to see factorizations when they're possible. 

Solving Quadratic Equations with the Quadratic Formula Problem Set 3  We now emphasize the Quadratic Formula, which always serves to solve for the roots of an equation of the form ax² + bx + c = 0.  
Solving Quadratic Equations with the Quadratic Formula Problem Set 4  The Quadratic Formula works every time on an equation of the form ax² + bx + c = 0.  
Solving Quadratic Equations with the Quadratic Formula Problem Set 5  The Quadratic Formula, which always serves to solve for the roots of an equation of the form ax² + bx + c = 0, should be practiced repeatedly.  
Solving Quadratic Equations  A Comprehensive Review  25 problems that can be solved using different techniques. Can you solve these problems before viewing the video? 

Solving Quadratic Equations by Completing the Square 

Title/Subject  Description  
Solving Quadratic Equations  A Comprehensive Review  25 problems that can be solved using different techniques. Can you solve these problems before viewing the video? 
Radical Expressions
Simplifying Radicals 


Title/Subject  Description  
Simplifying Radicals Sample Problem 1  To factor under the radical we have to know our facts of multiplication. We have to. 

Simplifying Radicals Sample Problem 2  We implore you NOT to use a calculator. This way, you can learn the language of numbers. To know radicals is not a radical idea, thank you. 

Adding and Subtracting Radical Expressions 

Title/Subject  Description  
Adding and Subtracting Radical Expressions Problem Set 1  As we manipulate the terms with radicals, we see the terms behave as if the radicals were letters, or variables, like "x."  
Adding and Subtracting Radical Expressions Problem Set 2  We simplify radical expressions by combining like terms. Radicals behave the same way that variables (or letters) behave. 

Adding and Subtracting Radical Expressions Problem Set 3  We simplify radical expressions and combine like terms. It is an acquired taste, and rather a game. 

Multiplying Radical Expressions 

Title/Subject  Description  
Multiplying Radical Expressions Problem Set 1  Easy Problems: In the multiplication of radicals we simplify where we can. Two negative factors, of course, result in a positive product. Learn to factor under the radical. 

Multiplying Radical Expressions Problem Set 2  MediumLevel Problems: As we multiply a radical times a binomial with radicals, we distribute across the binomial.  
Dividing Radical Expressions 

Title/Subject  Description  
Dividing Radical Expressions Problem Set 1  In this type of problems our goal is to rationalize the denominator.  
Dividing Radical Expressions Sample Problem Set 2  All levels of difficulty. This is a great way to practice the division of expressions. It helps to understand the factorization of the difference of two squares. 

Solving Radical Equations 

Title/Subject  Description  
Solving Radical Equations Sample Problem 1  We solve radical expressions for the value of the variable that makes each statement true.  
Using the Midpoint Formula 

Title/Subject  Description  
Midpoint Formula Sample Problem 1  1 Quadrants  Finding the Midpoint of a Line Segment in Cartesian Coordiantes is very easy. Here we stay in the First Quadrant with all values positive. 

Midpoint Formula Sample Problem 2  4 Quadrants  Finding the Midpoint of a Line Segment in Cartesian Coordiantes is very easy. Here we have Line Segments in all Four Quadrants. 
Rational Expressions
Simplifying Rational Expressions 


Title/Subject  Description  
Dividing Polynomials with Factoring Practice Problems 1  The polynomials in these problems will share factors. We factor out from numerator and denominator common factors, most often linear factors. 

Adding and Subtracting Rational Expressions 

Title/Subject  Description  
Adding and Subtracting Rational Expressions Problem Set 1  The technique to add Rational Expressions is to find the Common Denominator.  
Multiplying Rational Expressions 

Title/Subject  Description  
Multiplying Rational Expressions Problem Set 1  Not all problems have a similar degree of difficulty. But in any case, we can divide common factors topandbottom in rational expressions. 

Dividing Polynomials Rational Expressions 

Title/Subject  Description  
Dividing Polynomials Rational Expressions Problem Set 1  Here we divide a higherorder polynomial by a Linear Binomial. It's really just simple division. 

Solving Rational Equations 

Title/Subject  Description  
Solve Linear Equations with Fractions Problem Set 01  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 

Solve Linear Equations with Fractions Problem Set 02  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 

Solve Linear Equations with Fractions Problem Set 03  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 

Solve Linear Equations with Fractions Problem Set 04  Practice with basic expressions in x that involve fractions. All of our xterms are to the first power. This makes these equations linear. 
Systems of Equations
Solving Algebraically Two Variable Systems of Equations 


Title/Subject  Description  
Solving Algebraically Two Variable Systems of Equations Practice Problems  10 problems to solve system of equations by substitution. 

Solving Linear Equations in 1 Variable Practice Problems 1  In these problems we solve two linear equations, one on each side of the equal sign.  
Solving Linear Equations in 1 Variable Practice Problems 2  In these problems we solve two linear equations, one on each side of the equal sign.  
Solving Algebraically Two Variable Systems of Equations Problem Set 1  Solve linear pairs of equations in two variables. We begin with easy examples. The solutions are simultaneous. 

Solving Algebraically Two Variable Systems of Equations Problem Set 2  Elimination of a variable is a good technique to solve many pairs of linear equations in two variables. Generally we either add or subtract equations to eliminate one of the variables. 

Solving Algebraically Two Variable Systems of Equations Problem Set 3  Don't let fractions get in the way of solving equations. Just use what you have already learned. 

Solving Algebraically Two Variable Systems of Equations Problem Set 4  We give you a break with fewer fractions than the previous problem set. Relax and apply what you already know. 

Solving Algebraically Two Variable Systems of Equations Problem Set 5  Eliminate a variable. Distribute. Rewrite equations with substitutions. Solve. 

Solving Algebraically Two Variable Systems of Equations Problem Set 6  Find the values that make both statements true. There is (generally) a unique solution to a pair of linear equations. It is a simultaneous solution. 

Solving Algebraically Two Variable Systems of Equations Problem Set 7  Eliminate a variable. Solve for the unknowns. We may also isolate a variable and use the Substitution Method. 

Solving Algebraically Two Variable Systems of Equations Problem Set 8  Plug back in and rewrite the other equation as we solve linear equations. By now your techniques should be more comfortable. 

Solving Algebraically Two Variable Systems of Equations Problem Set 9  Multiply equations by different factors to get opposite coefficients on the same variable. Then eliminate a variable. Or substitute. Solve for the other. Then plug back in and rewrite. 

Solving Algebraically Two Variable Systems of Equations Problem Set 10  Sometimes we substitute. Sometimes we eliminate a variable. Solve for one and rewrite the other equation, then solve for the other variable. 

Solving Algebraically Two Variable Systems of Equations Problem Set 11  Watch your minus signs as we add equations to one another or subtract one equation from another.  
Solving Algebraically Two Variable Systems of Equations Problem Set 12  Multiply an equation through by a factor to eliminate a variable. Practice makes this a very easy proposition. Don't let the fractions throw you. Practice. 

Solving Algebraically Two Variable Systems of Equations Comprehensive Problem Set  Twentyfive problems. Mr. X will do them all. BUT YOU SHOULD DO THEM FIRST. 

Solving Graphically Two Variable Systems of Equations 

Title/Subject  Description  
Solving Graphically Two Variable Systems of Equations Problem Set 1  The intersection of two linear functions is the simultaneous solution to those equations.  
Solving Graphically Two Variable Systems of Equations Problem Set 2  Given two Linear Equations in Standard Form, we graphically solve for the simultaneous solution. It's easy if you can do the arithmetic. 
Systems of Equations
Solving Algebraically Two Variable Systems of Equations 


Title/Subject  Description  
Solving Algebraically Two Variable Systems of Equations Practice Problems  10 problems to solve system of equations by substitution. 

Solving Linear Equations in 1 Variable Practice Problems 1  In these problems we solve two linear equations, one on each side of the equal sign.  
Solving Linear Equations in 1 Variable Practice Problems 2  In these problems we solve two linear equations, one on each side of the equal sign.  
Solving Algebraically Two Variable Systems of Equations Problem Set 1  Solve linear pairs of equations in two variables. We begin with easy examples. The solutions are simultaneous. 

Solving Algebraically Two Variable Systems of Equations Problem Set 2  Elimination of a variable is a good technique to solve many pairs of linear equations in two variables. Generally we either add or subtract equations to eliminate one of the variables. 

Solving Algebraically Two Variable Systems of Equations Problem Set 3  Don't let fractions get in the way of solving equations. Just use what you have already learned. 

Solving Algebraically Two Variable Systems of Equations Problem Set 4  We give you a break with fewer fractions than the previous problem set. Relax and apply what you already know. 

Solving Algebraically Two Variable Systems of Equations Problem Set 5  Eliminate a variable. Distribute. Rewrite equations with substitutions. Solve. 

Solving Algebraically Two Variable Systems of Equations Problem Set 6  Find the values that make both statements true. There is (generally) a unique solution to a pair of linear equations. It is a simultaneous solution. 

Solving Algebraically Two Variable Systems of Equations Problem Set 7  Eliminate a variable. Solve for the unknowns. We may also isolate a variable and use the Substitution Method. 

Solving Algebraically Two Variable Systems of Equations Problem Set 8  Plug back in and rewrite the other equation as we solve linear equations. By now your techniques should be more comfortable. 

Solving Algebraically Two Variable Systems of Equations Problem Set 9  Multiply equations by different factors to get opposite coefficients on the same variable. Then eliminate a variable. Or substitute. Solve for the other. Then plug back in and rewrite. 

Solving Algebraically Two Variable Systems of Equations Problem Set 10  Sometimes we substitute. Sometimes we eliminate a variable. Solve for one and rewrite the other equation, then solve for the other variable. 

Solving Algebraically Two Variable Systems of Equations Problem Set 11  Watch your minus signs as we add equations to one another or subtract one equation from another.  
Solving Algebraically Two Variable Systems of Equations Problem Set 12  Multiply an equation through by a factor to eliminate a variable. Practice makes this a very easy proposition. Don't let the fractions throw you. Practice. 

Solving Algebraically Two Variable Systems of Equations Comprehensive Problem Set  Twentyfive problems. Mr. X will do them all. BUT YOU SHOULD DO THEM FIRST. 

Solving Graphically Two Variable Systems of Equations 

Title/Subject  Description  
Solving Graphically Two Variable Systems of Equations Problem Set 1  The intersection of two linear functions is the simultaneous solution to those equations.  
Solving Graphically Two Variable Systems of Equations Problem Set 2  Given two Linear Equations in Standard Form, we graphically solve for the simultaneous solution. It's easy if you can do the arithmetic. 
Trigonometry
Trigonometric Ratios 


Title/Subject  Description  
Trigonometric Ratios Problem Set 1  We calculate sines, cosines and tangents of different angles in triangles.  
Inverse Trigonometric Ratios 

Title/Subject  Description  
Inverse Trigonometric Ratios Problem Set 1  Inverse trig functions return the angle whose trig function is that number.  
Inverse Trigonometric Ratios Problem Set 2  Inverse trig functions return the angle whose trig function is that number.  
Solving Right Triangles 

Title/Subject  Description  
Solving Right Triangles Sample Problem Set 1  On these problems we determine the length of a side of a right triangle given two sides and one angle.  
MultiStep Problems 

Title/Subject  Description  
Calculating Trig Values from a Given Trig Value and the Associated Angle  Given a trig value and an associated angle, determine the values of the other five basic trig function values for that angle. 
Word Problems
One Step Equation Word Problems 


Title/Subject  Description  
One Step Equation Word Problems Problem Set 1  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 2  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 3  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 4  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 5  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
One Step Equation Word Problems Problem Set 6  Basic word problems with basic algebra are essentially arithmetic problems with an occasional letter or variable thrown into it.  
Two Step Equation Word Problems 

Title/Subject  Description  
Two Step Equation Word Problems Paired Worksheet  Work along Mr. X solving two step equation word problems. Download the worksheet before you play the video! 

Two Step Equation Word Problems Sample Problem 1  An illustrative example: The sum of two numbers is 60, and the greater is four times the less. What are the numbers? 

Two Step Equation Word Problems Sample Problem 2  A man bought a horse and carriage for $500, paying three times as much for the carriage as for the horse. How much did each cost? 

Two Step Equation Word Problems Sample Problem 3  For 72 cents Martha bought some needles and thread, paying eight times as much for the thread as for the needles. How much did she pay for each? 

Two Step Equation Word Problems Sample Problem 4  An illustrative example: What number added to twice itself and 40 more will make a sum equal to eight times the number?  
Two Step Equation Word Problems Sample Problem 5  James is 3 years older than William, and twice James's age is equal to three times William's age. What is the age of each? 

Two Step Equation Word Problems Sample Problem 6  Roger is onefourth as old as his father, and the sum of their ages is 70 years. How old is each? 

Two Step Equation Word Problems Sample Problem 7  An illustrative example: If the difference between two numbers is 48, and one number is five times the other, what are the numbers?  
Two Step Equation Word Problems Sample Problem 8  James gathered 12 quarts of nuts more than Henry gathered. How many did each gather if James gathered three times as many as Henry? 

Two Step Equation Word Problems Sample Problem 9  Mr. A is 48 years older than his son, but he is only three times as old. How old is each? 

Two Step Equation Word Problems Sample Problem 10  A man bought a hat, a pair of boots, and a necktie for $$7.50; the hat cost four times as much as the necktie, and the boots cost five times as much as the necktie. What was the cost of each? 

Two Step Equation Word Problems Sample Problem 11  There are 120 pigeons in three flocks. In the second there are three times as many as in the first, and in the third as many as in the first and second combined. How many pigeons in each flock? 

Two Step Equation Word Problems Sample Problem 12  Three men, A, B, and C, earned $110; A earned four times as much as B, and C as much as both A and B. How much did each earn? 

Two Step Equation Word Problems Sample Problem 13  A farmer bought a horse, a cow, and a calf for $72; the cow cost twice as much as the calf, and the horse three times as much as the cow. What was the cost of each? 

Two Step Equation Word Problems Sample Problem 14  A grocer sold one pound of tea and two pounds of coffee for $1.50, and the price of the tea per pound was three times that of the coffee. What was the price of each? 

Two Step Equation Word Problems Sample Problem 15  By will Mrs. Cabot was to receive five times as much as her son Henry. If Henry received $20,000 less than his mother, how much did each receive? 

Two Step Equation Word Problems Sample Problem 16  An illustrative example: Divide the number 126 into two parts such that one part is 8 more than the other.  
Two Step Equation Word Problems Sample Problem 17  At an election in which 1079 votes were cast the successful candidate had a majority of 95. How many votes did each of the two candidates receive? 

Two Step Equation Word Problems Sample Problem 18  John and Henry together have 143 marbles. If I should give Henry 15 more, he would have just as many as John. How many has each? 

Two Step Equation Word Problems Sample Problem 19  Two men whose wages differ by eight dollars receive both together $44 per hour. How much does each receive? 

Two Step Equation Word Problems Sample Problem 20  Divide 62 into three parts such that the first part is 4 more than the second, and the third 7 more than the second.  
Two Step Equation Word Problems Sample Problem 21  A man had 95 sheep in three flocks. In the first flock there were 23 more than in the second, and in the third flock 12 less than in the second. How many sheep in each flock? 

Two Step Equation Word Problems Sample Problem 22  A man owns three farms. In the first there are 5 acres more than in the second and 7 acres less than in the third. If there are 53 acres in all the farms together, how many acres are there in each farm? 

Two Step Equation Word Problems Sample Problem 23  Three firms lost $118,000 by fire. The second firm lost $6000 less than the first and $20,000 more than the third. What was each firm's loss? 

Two Step Equation Word Problems Sample Problem 24  In an orchard containing 33 trees the number of pear trees is 5 more than three times the number of apple trees. How many are there of each kind? 

Two Step Equation Word Problems Sample Problem 25  To the double of a number I add 17 and obtain as a result 147. What is the number? Also: To four times a number I add 23 and obtain 95. Also: From three times a number I take 25 and obtain 47. Also: Find a number which being multiplied by 5 and having 14 added to the product will equal 69. 

Two Step Equation Word Problems Sample Problem 26  I bought some tea and coffee for $10.39. If I paid for the tea 61 cents more than five times as much as for the coffee, how much did I pay for each? 

Two Step Equation Word Problems Sample Problem 27  Two houses together contain 48 rooms. If the second house has 3 more than twice as many rooms as the first, how many rooms has each house? 

Two Step Equation Word Problems Sample Problem 28  Mr. Ames builds three houses. The first cost $2000 more than the second, and the third twice as much as the first. If they all together cost $18,000, what was the cost of each house? 

Two Step Equation Word Problems Sample Problem 29  George bought an equal number of apples, oranges, and bananas for $1.08; each apple cost 2 cents, each orange 4 cents, and each banana 3 cents. How many of each did he buy? 

Two Step Equation Word Problems Sample Problem 30  A man bought 3 lamps and 2 vases for $6. If a vase cost 50 cents less than 2 lamps, what was the price of each? 

Two Step Equation Word Problems Sample Problem 31  Johnson and May enter into a partnership in which Johnson's interest is four times as great as May's. Johnson's profit was $4500 more than May's profit. What was the profit of each? 

Two Step Equation Word Problems Sample Problem 32  Divide 71 into three parts so that the second part shall be 5 more than four times the first part, and the third part three times the second.  
Two Step Equation Word Problems Sample Problem 33  I bought a certain number of barrels of apples and three times as many boxes of oranges for $33. I paid $2 a barrel for the apples, and $3 a box for the oranges. How many of each did I buy? 

Two Step Equation Word Problems Sample Problem 34  Divide the number 288 into three parts, so that the third part shall be twice the second, and the second five times the first.  
Two Step Equation Word Problems Sample Problem 35  If John's age be multiplied by 5, and if 24 be added to the product, the sum will be seven times his age. What is his age? 

Two Step Equation Word Problems Sample Problem 36  A man, being asked how many sheep he had, said, "If you will give me 24 more than six times what I have now, I shall have ten times my present number." How many had he?  
Two Step Equation Word Problems Sample Problem 37  Four dozen oranges cost as much as 7 dozen apples, and a dozen oranges cost 15 cents more than a dozen apples. What is the price of each? 

Two Step Equation Word Problems Sample Problem 38  A farmer pays just as much for 4 horses as he does for 6 cows. If a cow costs 15 dollars less than a horse, what is the cost of each? 

Two Step Equation Word Problems Sample Problem 39  Roger is onefourth as old as his father, and the sum of their ages is 70 years. How old is each? 

Two Step Equation Word Problems Sample Problem 40  Jane is onefifth as old as Mary, and the difference of their ages is 12 years. How old is each? 

Two Step Equation Word Problems Sample Problem 41  Two men own a third and twofifths of a mill respectively. If their part of the property is worth $22,000, what is the value of the mill? 

Two Step Equation Word Problems Sample Problem 42  In three pastures there are 42 cows. In the second there are twice as many as in the first, and in the third there are onehalf as many as in the first. how many cows are there in each pasture? 

Two Step Equation Word Problems Sample Problem 43  What number increased by threesevenths of itself will amount to 8640?  
Two Step Equation Word Problems Sample Problem 44  There are three numbers whose sum is 90; the second is equal to onehalf of the first, and the third is equal to the second plus three times the first. What are the numbers? 

Two Step Equation Word Problems Sample Problem 45  A grocer sold 62 pounds of tea, coffee, and cocoa. Of tea he sold 2 pounds more than of coffee, and of cocoa 4 pounds more than of tea. How many pounds of each did he sell? 

Two Step Equation Word Problems Sample Problem 46  John has oneninth as much money as Peter, but if his father should give him 72 cents, he would have just the same as Peter. How much money has each boy? 

Two Step Equation Word Problems Sample Problem 47  Two boys picked 26 boxes of strawberries. If John picked fiveeighths as many as Henry, how many boxes did each pick? 

Two Step Equation Word Problems Sample Problem 48  In a school containing 420 pupils, there are threefourths as many boys as girls. How many are there of each? 

Two Step Equation Word Problems Sample Problem 49  One man carried off threesevenths of a pile of soil, another man fourninths of the pile. In all they took 110 cubic yards of earth. How large was the pile at first? 

Two Step Equation Word Problems Sample Problem 50  Matthew had three times as many stamps as Herman, but after he had lost 70, and Herman had bought 90, they put what they had together and found that they had 540 stamps. How many had each at first? 

Distance, Rate, and Time Word Problems 

Title/Subject  Description  
Distance, Rate, and Time Word Problems 1  Distance equals Rate times Time. This basic relationship needs to be reinforced with lots of practice. 

Distance, Rate, and Time Word Problems 2  Distance equals Rate times Time. Distance divided by Rate equals Time. Distance divided by Time is the Rate, or Speed. 

Work Word Problems 

Title/Subject  Description  
Solving Basic Equations 08  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Solving Basic Equations 12  More practice with simple and basic equations in one variable. We show some problem solutions more than one way. 

Two Step Equation Word Problems Sample Problem 15  By will Mrs. Cabot was to receive five times as much as her son Henry. If Henry received $20,000 less than his mother, how much did each receive? 

Two Step Equation Word Problems Sample Problem 19  Two men whose wages differ by eight dollars receive both together $44 per hour. How much does each receive? 

Two Step Equation Word Problems Sample Problem 23  Three firms lost $118,000 by fire. The second firm lost $6000 less than the first and $20,000 more than the third. What was each firm's loss? 