Problem 15 · 2020 AMC 8
Easy
Fractions, Decimals & Percents
percent-multiplier
Suppose 15% of x equals 20% of y. What percentage of x is y?
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Answer: C — 75%.
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Hint 1 of 2
“What percent of x is y?” is asking for y ÷ x. So your goal is to get y alone in terms of x — watch the direction so you don't flip them.
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Hint 2 of 2
Turn the percents into decimals: 0.15x = 0.20y. Solving for y gives y as a multiple of x, and that multiple is the answer.
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Approach: rearrange to y = (something) × x
- “What percent of x is y?” means find y ÷ x — so isolate y in terms of x.
- 0.15x = 0.20y ⇒ y = 0.150.20 x = 0.75x, so y is 75% of x.
- Watch the direction: the question fixes x as the base (“percent of x”), so the answer is y/x. Flipping it would give 133⅓%, which is the trap choice. Always reread which quantity is the ‘of’.
Another way — pick a concrete number:
- Let 15% of x = 20% of y = 60 (any shared value works). Then x = 60 ÷ 0.15 = 400 and y = 60 ÷ 0.20 = 300.
- y as a percent of x: 300/400 = 75%. Plugging in real numbers makes ‘percent of which one’ impossible to flip by accident.
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