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Algebra Word Problems Practice

Fifteen hand-built word problems that turn into linear equations, with complete solutions. Each one shows how to choose the variable, translate the sentence into an equation, solve it, and check the answer against the words.

  1. 1.

    Six more than three times a number is 27. Find the number.

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    Let be the number.

    Check: . ✓ The number is .

  2. 2.

    The sum of two consecutive integers is 85. Find them.

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    Let the smaller be ; the next is .

    The integers are and .

  3. 3.

    One number is 7 more than another. Their sum is 51. Find both numbers.

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    Let be the smaller; the larger is .

    The numbers are and .

  4. 4.

    A 90-cm wire is cut into two pieces so that one piece is 4 times the length of the other. Find both lengths.

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    Let be the shorter piece; the longer is .

    The pieces are cm and cm.

  5. 5.

    Three times a number, decreased by 5, is the same as the number increased by 11. Find the number.

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    The number is .

  6. 6.

    Ten less than four times a number equals twice the number plus 8. Find the number.

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    The number is .

  7. 7.

    The sum of three consecutive even integers is 138. Find them.

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    The integers are , , and .

  8. 8.

    The sum of three consecutive odd integers is 165. Find them.

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    The integers are , , and .

  9. 9.

    The larger of two numbers is 3 less than 4 times the smaller. Their sum is 42. Find both.

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    Let be the smaller; the larger is .

    The numbers are and .

  10. 10.

    The sum of four consecutive integers is 130. Find them.

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    The integers are , , , .

  11. 11.

    A jar of dimes and quarters has 3 times as many dimes as quarters, and 40 coins total. How many of each?

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    Let be the quarters; dimes are .

    quarters and dimes.

  12. 12.

    A box holds 54 pens, all blue or black. There are 6 more black pens than twice the number of blue pens. How many of each?

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    Let be the blue pens; black is .

    There are blue and black. Check: . ✓

  13. 13.

    A mother is 4 times as old as her daughter. In 16 years she will be twice as old as the daughter is then. Find their current ages.

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    Let be the daughter's age now; the mother is .

    The daughter is ; the mother is . In 16 years: and , and . ✓

  14. 14.

    Kim is 5 years older than Lee. Three years ago, Kim was twice as old as Lee was then. Find their current ages.

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    Let be Lee's age now; Kim is . Three years ago: Lee was , Kim was .

    Lee is , Kim is . Check three years ago: and . ✓

  15. 15.

    Twice the sum of a number and 4 is 6 more than the number. Find the number.

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    The number is . Check: and . ✓
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MPhil in Mathematics, Founder of Mathovia
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Mathematics verification: Mathematical formulas, calculations, worked examples and solutions are reviewed for accuracy before publication. How we check our work

Algebra Word Problems Practice

The Word Problems lesson gives a five-step method and a full translation table; this set is 15 problems to practice it on, each with a complete worked solution.

How to use this set

Work each one on paper first — choose the variable, write the equation, solve, and check. The value is in the setup, so write out every step. Type your answer in the box and press Check Answers. When a problem asks for two or three values, separate them with commas in any order — 42, 43 and 43, 42 both count, and units like cm are ignored.

Common mistakes to watch for

Using a different letter for every unknown. One variable with expressions needs only one equation.

Reversing a subtraction. “7 less than ” is , not .

Forgetting parentheses after “the sum of… , doubled.” , not .

Stopping at . If the question asks for the largest integer or the number of dimes, translate back.

Where to go next

For the specialized types, see the Distance, Rate, and Time Practice Problems, Work Problems Practice Problems, and Mixture Problems Practice Problems. For the full method, see the Word Problems lesson.

Frequently Asked Questions

How is this practice set organized?+

It is a hand-written set of 15 problems rather than auto-generated ones, because word problems don't translate into a single auto-checkable number. Each problem has a full worked solution you can open after attempting it.

What is the hardest part of a word problem?+

The translation — reading the sentence and writing the right equation. Once the equation is written, it is solved with ordinary linear-equation techniques.

How do I choose what x represents?+

Let be the simplest unknown, phrased plainly, and write every other unknown as an expression in that same . Two separate letters would need two equations.

Why check the answer against the words and not just the equation?+

A value can solve the equation but be impossible in context — a negative age, a fractional person. That means the equation was set up wrong, so you fix the translation, not the arithmetic.

How do age problems work?+

Everyone ages at the same rate. Set up 'now' ages first, then shift both people by the same number of years for a past or future condition.

Are the motion, work, and mixture word problems here?+

No — those have their own dedicated practice sets. This set covers number, age, consecutive-integer, and part-of-a-whole problems.

What if the question asks for two numbers?+

Type both, separated by a comma. Order is not checked, so 42, 43 and 43, 42 are equally correct, and you can leave units off — 18, 72 and 18 cm, 72 cm both pass. Where only one number is wanted, just type that.

More practice problems

Distance, Rate, and Time Practice Problems Work Rate Practice Problems Mixture Word Problems Practice