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2018 AMC 12A Problem 1

Problem 1 of 25EasierAlgebra

A large urn contains 100100 balls, of which 36%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%?72\%? (No red balls are to be removed.)

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Solution

There are 3636 red balls, and this count stays fixed. For the red balls to be 72%72\% of the urn, the urn must contain 36÷0.72=5036 \div 0.72 = 50 balls. Since 100−50=50100 - 50 = 50, exactly 5050 blue balls are removed. Thus, the correct answer is D.

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Concepts: percentage

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.