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2015 AMC 12A Problem 4

Problem 4 of 25EasierAlgebraArithmetic

The sum of two positive numbers is 55 times their difference. What is the ratio of the larger number to the smaller number?

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Solution

Let xx and yy be the numbers with x>y>0.x \gt y \gt 0. Then x+y=5(x−y).x+y = 5(x-y). Expanding gives x+y=5x−5y,x+y = 5x-5y, so 6y=4x6y = 4x and xy=32.\dfrac{x}{y} = \dfrac{3}{2}. Thus, the correct answer is B.
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Tagged: ratio and proportion · linear equation

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