2015 AMC 10A Problems/Problem 6

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Problem

The sum of two positive numbers is $5$ times their difference. What is the ratio of the larger number to the smaller number?

$\textbf{(A)}\ \frac{5}{4}\qquad\textbf{(B)}\ \frac{3}{2}\qquad\textbf{(C)}\ \frac{9}{5}\qquad\textbf{(D)}}\ 2 \qquad\textbf{(E)}\ \frac{5}{2}$ (Error compiling LaTeX. ! Extra }, or forgotten $.)

Solution

Let $a$ be the bigger number and $b$ be the smaller.

$a + b = 5(a - b)$.

Solving gives $\fracab = \frac32$ (Error compiling LaTeX. ! Undefined control sequence.), so the answer is \boxed{\textbf{(B) }\frac32}$.

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