2015 AMC 10A Problem 6

Question

The sum of two positive numbers is

5

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

\dfrac{5}{4}

\dfrac{3}{2}

\dfrac{9}{5}

2

\dfrac{5}{2}

Let the larger number be

L

and the smaller be

S

Simplify

L+S=5(L-S)

Let

x

and

y

be the two numbers. Then we have that

x + y = 5(x - y).

Note that we are assuming

x \gt y.

This gives us

x + y = 5x - 5y

6y = 4x.

Dividing through yields

\dfrac{x}{y} = \dfrac{6}{4} = \dfrac{3}{2}.

Thus, B is the correct answer.

Problem 6 in other years