2015 AMC 10A Problems/Problem 6

Problem

The sum of two positive numbers is 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. Unknown error_msg)

Solution

Let be the bigger number and be the smaller.

.

Solving gives , so the answer is .