# 2015 AMC 10A Problems/Problem 6

The following problem is from both the 2015 AMC 12A #4 and 2015 AMC 10A #6, so both problems redirect to this page.

## Problem

The sum of two positive numbers is $5$ times their difference. What is the ratio of the larger number to the smaller number? $\textbf{(A)}\ \frac{5}{4}\qquad\textbf{(B)}\ \frac{3}{2}\qquad\textbf{(C)}\ \frac{9}{5}\qquad\textbf{(D)}\ 2 \qquad\textbf{(E)}\ \frac{5}{2}$

## Solution

Let $a$ be the bigger number and $b$ be the smaller. $a + b = 5(a - b)$.

Multiplying out gives $a + b = 5a - 5b$ and rearranging gives $4a = 6b$ and then solving gives $\frac{a}{b} = \frac32$, so the answer is $\boxed{\textbf{(B) }\frac32}$.

~savannahsolver

## See Also

 2015 AMC 10A (Problems • Answer Key • Resources) Preceded byProblem 5 Followed byProblem 7 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 10 Problems and Solutions
 2015 AMC 12A (Problems • Answer Key • Resources) Preceded byProblem 3 Followed byProblem 5 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 12 Problems and Solutions

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