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AlgebraVery hardSmaller number from a sum-to-difference ratio

Algebra practice question

The sum of two numbers is three times their difference, and the larger number is 12. What is the smaller number?

Answer: 6

12 + y = 3(12 − y) gives 12 + y = 36 − 3y, so 4y = 24 and y = 6.

Common wrong answers

If you answered 3
3 halves 6.
If you answered 4
4 is 12 ÷ 3.
If you answered 9
9 comes from 12 + y = 3(12) − y.

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