AlgebraHardFractional parts of an unknown number
Algebra practice question
Two thirds of a number is 12 more than one quarter of the same number. What is the number?
Answer: 144/5 or 28.8
Let the number be n: (2/3)n − (1/4)n = 12. The left side is (8/12 − 3/12)n = (5/12)n, so n = 12 × 12/5 = 144/5 = 28.8.
Common wrong answers
- If you answered 5
- 5 comes from 12 ÷ (12/5), inverting the fraction the wrong way.
- If you answered 18
- 18 comes from (2/3)n = 12, ignoring the one-quarter part.
- If you answered 144
- 144 is 12 × 12, before dividing by 5.
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