Algebra Word Problems Practice (Age, Coin and Number Problems)

How it works

A reliable routine:

Name the unknown. Write "let d = the daughter's age now". Pick the quantity that makes the others easy to write.
Write everything else in terms of it. Mother = 5d. In 12 years: d + 12 and 5d + 12.
Find the sentence that gives an equation. "She will be twice as old" means 5d + 12 = 2(d + 12).
Solve and answer the question asked, which may not be the variable itself. Check it against the original words.

Useful translations: "is" means =, "of" means ×, "decreased by" means −, and "three consecutive integers" are n, n + 1, n + 2.

These problems come from Mathyessy's question bank. Try each one before opening the solution.

3 times a number, decreased by 2, is 22. What is the number?
Show answer and solution
Answer: 8
3n − 2 = 22, so 3n = 24 and n = 8.
4 coins are nickels and dimes worth 35 cents. How many dimes are there?
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Answer: 3 dimes
Let d be the number of dimes, so there are 4 − d nickels. 10d + 5(4 − d) = 35 gives 5d + 20 = 35, so d = 3. (3 dimes and 1 nickel make 35¢.)
A mother is 5 times as old as her daughter. In 12 years she will be twice as old. How old is the daughter now?
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Answer: 4
Daughter d, mother 5d. In 12 years: 5d + 12 = 2(d + 12) = 2d + 24. So 3d = 12 and d = 4. Check: 20 and 4 now; 32 and 16 later.
The sum of three consecutive integers is 12. What is the smallest?
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Answer: 3
n + (n + 1) + (n + 2) = 3n + 3 = 12, so n = 3. The integers are 3, 4, 5.

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