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 lessons and problems are included with a subscription to Mr. X.

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Basic Algebra Sample Problem 1

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Basic Algebra Problem Set

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Title	Description
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. Simplify the radicals.
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 √45 = √9 times √5, or 3 times √5.
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. How many votes did each of the two candidates receive?
Basic Algebra Problem 56	John and Henry together have 143 marbles. If I should give Henry 15 more, he would have just as many as John. How many has each?
Basic Algebra Problem 57	Two men whose wages differ by eight dollars receive both together $44 per hour. How much does each receive?
Basic Algebra Problem 58	Divide 62 into three parts such that the first part is 4 more than the second, and the third 7 more than the second.
Basic Algebra Problem 59	A man had 95 sheep in three flocks. In the first flock there were 23 more than in the second, and in the third flock 12 less than in the second. How many sheep in each flock?
Basic Algebra Problem 60	A man owns three farms. In the first there are 5 acres more than in the second and 7 acres less than in the third. If there are 53 acres in all the farms together, how many acres are there in each farm?
Basic Algebra Problem 61	Three firms lost $118,000 by fire. The second firm lost $6000 less than the first and $20,000 more than the third. What was each firm's loss?
Basic Algebra Problem 62	In an orchard containing 33 trees the number of pear trees is 5 more than three times the number of apple trees. How many are there of each kind?
Basic Algebra Problem 64	To the double of a number I add 17 and obtain as a result 147. What is the number? Also: To four times a number I add 23 and obtain 95. Also: From three times a number I take 25 and obtain 47. Also: Find a number which being multiplied by 5 and having 14 added to the product will equal 69.
Basic Algebra Problem 66	I bought some tea and coffee for $10.39. If I paid for the tea 61 cents more than five times as much as for the coffee, how much did I pay for each?
Basic Algebra Problem 67	Two houses together contain 48 rooms. If the second house has 3 more than twice as many rooms as the first, how many rooms has each house?
Basic Algebra Problem 68	Mr. Ames builds three houses. The first cost $2000 more than the second, and the third twice as much as the first. If they all together cost $18,000, what was the cost of each house?
Basic Algebra Problem 70	George bought an equal number of apples, oranges, and bananas for $1.08; each apple cost 2 cents, each orange 4 cents, and each banana 3 cents. How many of each did he buy?
Basic Algebra Problem 72	A man bought 3 lamps and 2 vases for $6. If a vase cost 50 cents less than 2 lamps, what was the price of each?
Basic Algebra Problem 73	Johnson and May enter into a partnership in which Johnson's interest is four times as great as May's. Johnson's profit was $4500 more than May's profit. What was the profit of each?
Basic Algebra Problem 74	Divide 71 into three parts so that the second part shall be 5 more than four times the first part, and the third part three times the second.
Basic Algebra Problem 75	I bought a certain number of barrels of apples and three times as many boxes of oranges for $33. I paid $2 a barrel for the apples, and $3 a box for the oranges. How many of each did I buy?
Basic Algebra Problem 76	Divide the number 288 into three parts, so that the third part shall be twice the second, and the second five times the first.
Basic Algebra Problem 77	If John's age be multiplied by 5, and if 24 be added to the product, the sum will be seven times his age. What is his age?
Basic Algebra Problem 78	A man, being asked how many sheep he had, said, "If you will give me 24 more than six times what I have now, I shall have ten times my present number." How many had he?
Basic Algebra Problem 79	Four dozen oranges cost as much as 7 dozen apples, and a dozen oranges cost 15 cents more than a dozen apples. What is the price of each?
Basic Algebra Problem 80	A farmer pays just as much for 4 horses as he does for 6 cows. If a cow costs 15 dollars less than a horse, what is the cost of each?
Basic Algebra Problem 81	Roger is 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.
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.
Powers and Roots	Six little problems help us to understand roots and exponents.
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.
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. Sometimes we show more than one way to solve.
Solving Basic Equations 11	When solutions are obvious, we recommend you simply write the answer. We practice cancelling factors "top and bottom" in fractions.
Solving Basic Equations 12	Combine like terms. Cancel factors top and bottom. Distribute over binomials. See different ways to solve simple equations in one variable.
Solving Basic Equations 13	A comprehensive review of basic problems. Fifty simple problems. I'll do the odds.
Solving Basic Linear Equations 14	Solve linear pairs of equations in two variables. We begin with easy examples. The solutions are simultaneous.
Solving Basic Linear Equations 15	Elimination of a variable is a good technique to solve many pairs of linear equations in two variables. Generally we either add or subtract equations to eliminate one of the variables.
Solving Basic Linear Equations 16	Don't let fractions get in the way of solving equations. Just use what you have already learned.
Solving Basic Linear Equations 17	We give you a break with fewer fractions than the previous problem set. Relax and apply what you already know.
Solving Basic Linear Equations 18	Eliminate a variable. Distribute. 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. quadratics.
Solving Basic Quadratic Equations 28	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 ax² + 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.
Solving Basic Quadratic Equations 30	We're factoring more quadratics. Coefficients with many factors give us reason to scratch our heads just a little.
Solving Basic Quadratic Equations 31	Factoring second-order polynomials in one variable (quadratics) into linear factors, or binomials. We employ a variety of techniques.
Solving Basic Quadratic Equations 32	More factoring of quadratics. Practice and knowing facts of arithmetic are key. We look briefly at a graph from Wolfram Alpha.
Solving Basic Quadratic Equations 33	Not every quadratic equation factors into neat binomials or linear factors. In such cases we use the Quadratic Formula.
Solving Basic Quadratic Equations 34	Factor, if possible. If the quadratic will not factor, use the Quadratic Formula. Build experience to see factorizations when they're possible.
Solving Basic Quadratic Equations 35	We now emphasize the Quadratic Formula, which always serves to solve for the roots of an equation of the form ax² + bx + c = 0.
Solving Basic Quadratic Equations 36	The Quadratic Formula works every time on an equation of the form ax² + bx + c = 0.
Solving Basic Quadratic Equations 37	Factor (if possible) or use the Quadratic Formula. We're keeping things real at this point.
Solving Basic Quadratic Equations 38	We introduce the complex solution when our quadratic has a negative discriminant. If this is beyond the scope of your work in Basic Algebra, that's just fine. Don't worry about it.
Solving Basic Quadratic Equations 39	Twenty-five problems, all solved for you, for quadratics of all kinds (mostly basic). You should work them before watching the video.