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2000 AMC 10 Problem 8

Problem 8 of 25EasierAlgebra

At Olympic High School, 25\tfrac25 of the freshmen and 45\tfrac45 of the sophomores took the AMC 10.10. Given that the number of freshmen and sophomore contestants was the same, which of the following must be true?

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Solution

Let ff and ss be the numbers of freshmen and sophomores. The contestant counts are equal, so 25f=45s.\tfrac25 f = \tfrac45 s. Multiplying by 55 gives 2f=4s,2f = 4s, so f=2s.f = 2s. There are twice as many freshmen as sophomores. Thus, the correct answer is D.

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Concepts: ratio and proportion · linear equation

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