AlgebraHardTwo numbers from a sum and a division with remainder
Algebra practice question
The sum of two positive integers is 40. When the larger is divided by the smaller, the quotient is 3 and the remainder is 4. What is the larger integer?
Answer: 31
Let the smaller be s: the larger is 3s + 4, and s + 3s + 4 = 40 → 4s = 36 → s = 9. The larger is 3(9) + 4 = 31.
Common wrong answers
- If you answered 9
- 9 is the smaller integer.
- If you answered 27
- 27 is 3 × 9, forgetting the remainder.
- If you answered 34
- 34 comes from 4s = 40 → s = 10, ignoring the remainder in the sum.
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