2018 AMC 12A Problem 1

Below is the professionally curated solution for Problem 1 of the 2018 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 12A solutions, or check the answer key.

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Concepts:percentage

Difficulty rating: 890

A large urn contains $100$ balls, of which $36\%$ are red and the rest are blue. How many of the blue balls must be removed so that the percentage of red balls in the urn will be $72\%?$ (No red balls are to be removed.)

$28$

$32$

$36$

$50$

$64$

Solution:

There are $36$ red balls, and this count stays fixed. For the red balls to be $72\%$ of the urn, the urn must contain $36 \div 0.72 = 50$ balls. Since $100 - 50 = 50$ , exactly $50$ blue balls are removed.

Thus, the correct answer is D.

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