Problem 22 · 2021 Math Kangaroo
Stretch
Fractions, Decimals & Percents
Algebra & Patterns
percent-multiplier
In a particular fraction the numerator and denominator are both positive. The numerator of this fraction is increased by 40%. By what percentage should its denominator be decreased so that the new fraction is double the original fraction?
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Answer: C — 30%
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Hint 1 of 2
Increasing the top by 40% multiplies the fraction by 1.4; you want the new fraction to be twice the old.
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Hint 2 of 2
Find the multiplier the denominator needs, then convert it to a percent decrease.
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Approach: balance the multipliers on top and bottom
- Multiplying the numerator by 1.4 while dividing the denominator by (1 − p) should double the fraction: 1.4 / (1 − p) = 2.
- So 1 − p = 0.7, giving p = 0.3.
- The denominator must drop by 30%.
- So the answer is C.
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