AMC10 2015 10A, Problem 6

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

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 factorised into $2a = 3b$ and then solving gives $\frac{a}{b} = \frac32$, so the answer is $\fbox{\frac{3}{2}}$.

Answer: \frac{3}{2}