2015 AMC 12A Problem 4

Problem 4 of 25EasierAlgebra

The sum of two positive numbers is

5

times their difference. What is the ratio of the larger number to the smaller number?

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Solution

Let

x

and

y

be the numbers with

x \gt y \gt 0.

Then

x+y = 5(x-y).

Expanding gives

x+y = 5x-5y,

6y = 4x

and

\dfrac{x}{y} = \dfrac{3}{2}.

Thus, the correct answer is B.

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.