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2015 AMC 10A Problem 6

Problem 6 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 two numbers. Then we have that x+y=5(x−y). x + y = 5(x - y). Note that we are assuming x>y.x \gt y. This gives us x+y=5x−5y x + y = 5x - 5y 6y=4x. 6y = 4x. Dividing through yields xy=64=32.\dfrac{x}{y} = \dfrac{6}{4} = \dfrac{3}{2}. Thus, B is the correct answer.
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Tagged: linear equation · ratio and proportion

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