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2012 AMC 12B Problem 4

Problem 4 of 25EasierAlgebra

Suppose that the euro is worth 1.301.30 dollars. If Diana has 500500 dollars and Étienne has 400400 euros, by what percent is the value of Étienne’s money greater than the value of Diana’s money?

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Solution

Étienne’s money is worth 400⋅1.30=520400\cdot1.30=520 dollars, while Diana has 500500 dollars. The percent by which Étienne’s value exceeds Diana’s is 520−500500⋅100%=4%.\frac{520-500}{500}\cdot100\%=4\%. Thus, the correct answer is B.

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Concepts: percentage · unit conversion

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