## 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 Sample Problem 3

# 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 absent-minded, or second-nature 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
One-Step 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
One-Step 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
One-Step 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.
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 one-fourth 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.
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.
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 one-fourth 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 one-fifth 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 two-fifths 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 one-half 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 three-sevenths 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 one-half 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 one-ninth 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 five-eighths 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 three-fourths as many boys as girls.
How many are there of each?
Two Step Equation Word Problems Sample Problem 49 One man carried off three-sevenths of a pile of soil, another man four-ninths 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 first-power 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 first-power 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 first-power 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 first-power 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 first-power 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 x-terms 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 x-terms 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 x-terms 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 x-terms 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.
One-Step 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
One-Step 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
One-Step 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 first-power 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 first-power 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 first-power 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 first-power 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 first-power 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 x-terms 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 x-terms 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 x-terms 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 x-terms 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.
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 one-fourth 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.
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.
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 one-fourth 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 one-fifth 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 two-fifths 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 one-half 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 three-sevenths 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 one-half 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 one-ninth 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 five-eighths 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 three-fourths as many boys as girls.
How many are there of each?
Two Step Equation Word Problems Sample Problem 49 One man carried off three-sevenths of a pile of soil, another man four-ninths 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.
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 Plug-and-chug 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 Math-Aids.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 second-nature 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 Math-Aids.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 Math-Aids.com, a worksheet to practice turning English into math.
Go to Math-Aids.com and build your own math worksheets to practice.
Algebra Translated 33 From Math-Aids.com, a worksheet to practice turning English into math.
Go to Math-Aids.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 Math-Aids.com
Basic Algebra Problem 112 The idea of this worksheet from math-Aids.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 math-Aids.com.
Basic Algebra Problem 114 Plotting pints involves matching up sets of ordered pairs.
Keep the x-coordinate and the y-coordinate straight, and it's a snap.
Basic Algebra Problem 115 From Math-Aids.com we have a worksheet with square roots.
Basic Algebra Problem 116 This worksheet from math-Aids.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 Math-Aids.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 Math-Aids.com is a sheet for function tables.
We generate y-values for a given simple function.
The x-values are inputs to the function.
Basic Algebra Problem 122 Given x-values, we figure out the y-values for these linear relations, or functions.
The lines on this particular worksheet each pass through the origin (0, 0).
Basic Algebra Problem 123 From Math-Aids: They provide the x-value.
We want to come up with the y-value based on the linear relationship given for each function.
Basic Algebra Problem 124 From our good friends at Math-Aids.com, we generate ordered pairs for x-y tables, for linear functions.
Basic Algebra Problem 125 Complete the table, from Math-Aids.com, for y-values for a given function and set of x-values.
Basic Algebra Problem 126 Once again, we're given the x-coordinate for points on a line, and we generate the y-value, or the output of the function for each x input.
Basic Algebra Problem 127 Complete the function tables in a worksheet from Math-Aids.com.
Basic Algebra Problem 128 This worksheet from math-Aids.com has "In and Out Boxes" that are another form of x-y tables for functions.
Basic Algebra Problem 129 More In-and-Out-Boxes.
We just follow what the functions tell us to do, from Math-Aids.
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 In-and-Out Boxes, from Math-Aids.com.
These are a snap if you know basic facts of arithmetic.
Basic Algebra Problem 131 We're talking about functions with these In-and-Out 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 In-and-Out Boxes for inputs and outputs, x and y, respectively.
Basic Algebra Problem 133 Just follow the recipe for these functions in this worksheet from Math-Aids.com, for inputs and outputs, for the independent variable and the dependent variable.
Basic Algebra Problem 134 In-and-Out 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 Math-Aids.com.
Our In-and-Out 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 one-fourth 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.
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.
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 one-fourth as old as his father, and the sum of their ages is 70 years.
How old is each?
Basic Algebra Problem 82 Jane is one-fifth 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 two-fifths 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 one-half as many as in the first.
how many cows are there in each pasture?
Basic Algebra Problem 87 What number increased by three-sevenths of itself will amount to 8640?
Basic Algebra Problem 88 There are three numbers whose sum is 90; the second is equal to one-half 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 one-ninth 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 five-eighths as many as Henry, how many boxes did each pick?
Basic Algebra Problem 94 In a school containing 420 pupils, there are three-fourths as many boys as girls.
How many are there of each?
Basic Algebra Problem 95 One man carried off three-sevenths of a pile of soil, another man four-ninths 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 Math-Aids.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 math-Aids.com, find the measure of the missing angle given three of the interior angles of a four-sided 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 Math-Aids.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 first-power 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 x-terms are to the first power.
This makes these equations linear.
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 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 odd-numbered 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.
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.
Re-write 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 re-write 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 re-write.
Solving Basic Linear Equations 23 Sometimes we substitute.
Sometimes we eliminate a variable.
Solve for one and re-write 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 Twenty-five problems.
I'll do them all.
BUT YOU SHOULD DO THEM FIRST.
Solving Basic Quadratic Equations 27 A problem set in factoring second-order polynomials in one variable, i.e.
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 second-order polynomials into linear factors.
Coefficients with many factors give us reason to scratch our heads just a little.
Solving Basic Quadratic Equations 31 Factoring second-order polynomials in one variable (quadratics) into linear factors, or binomials.
We employ a variety of techniques.
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.
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.
Solving Basic Quadratic Equations 39 Twenty-five 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 Math-Aids.com, a worksheet to translate algebraic expressions with two real values and one variable.
Translate Algebraic Expressions 14001 From Math-Aids.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 one-step 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 One-step 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 Two-step 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 One-step 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 one-step 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 Two-step 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.

### 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 Y-intercept from a Linear Equation

Title/Subject Description
Finding Slope and Y-intercept 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 Y-intercept from a Linear Equation Problem Set 2 Each of the equations in this video are already in the Slope-Intercept Form for the Equation of Line.
We just read the values of "m" and "b."
Finding Slope and Y-intercept 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 Slope-Intercept Form

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

### Graphing Lines Given Y-Intercept and an Ordered Pair

Title/Subject Description
Graphing Lines given Y-Intercept and an Ordered Pair Problem Set 1 We graph the line (segment) that contains both given points.
The y-intercept has an x-coordinate of zero.
Graphing Lines given Y-Intercept and an Ordered Pair Problem Set 2 Two points determine a line.
Here we also get the equation of the line in slope-intercept 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.

### 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 Slope-Intercept 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 Slope-Intercept 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.

### 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 Y-Intercept from a Linear Equation

Title/Subject Description
Finding Slope and Y-intercept 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 Y-intercept from a Linear Equation Problem Set 2 Each of the equations in this video are already in the Slope-Intercept Form for the Equation of Line.
We just read the values of "m" and "b."
Finding Slope and Y-intercept 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 Slope-Intercept Form

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

### 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 Slope-Intercept 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 Slope-Intercept 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 highest-degree 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 highest-degree 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 second-nature 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."

Title/Subject Description
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 a2 - b2 = (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 "non-factorable" 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 highest-degree 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 second-nature 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 second-nature to you.
But you have to practice. And you have to know your facts from the Times Table.

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.

Title/Subject Description

### 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 second-order polynomials in one variable, i.e.
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 second-order 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 second-order 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?

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.
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?

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.

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."
Radicals behave the same way that variables (or letters) behave.
It is an acquired taste, and rather a game.

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 Medium-Level Problems: As we multiply a radical times a binomial with radicals, we distribute across the binomial.

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.

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 top-and-bottom in rational expressions.

### Dividing Polynomials Rational Expressions

Title/Subject Description
Dividing Polynomials Rational Expressions Problem Set 1 Here we divide a higher-order 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 x-terms 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 x-terms 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 x-terms 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 x-terms 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.
Re-write 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 re-write 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 re-write.
Solving Algebraically Two Variable Systems of Equations Problem Set 10 Sometimes we substitute.
Sometimes we eliminate a variable.
Solve for one and re-write 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 Twenty-five 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.
Re-write 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 re-write 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 re-write.
Solving Algebraically Two Variable Systems of Equations Problem Set 10 Sometimes we substitute.
Sometimes we eliminate a variable.
Solve for one and re-write 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 Twenty-five 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.

### Multi-Step 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.
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 one-fourth 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.
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.
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 one-fourth 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 one-fifth 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 two-fifths 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 one-half 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 three-sevenths 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 one-half 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 one-ninth 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 five-eighths 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 three-fourths as many boys as girls.
How many are there of each?
Two Step Equation Word Problems Sample Problem 49 One man carried off three-sevenths of a pile of soil, another man four-ninths 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.