1980 AHSME Problems/Problem 3

Problem

If the ratio of $2x-y$ to $x+y$ is $\frac{2}{3}$ , what is the ratio of $x$ to $y$ ?

$\text{(A)} \ \frac{1}{5} \qquad \text{(B)} \ \frac{4}{5} \qquad \text{(C)} \ 1 \qquad \text{(D)} \ \frac{6}{5} \qquad \text{(E)} \ \frac{5}{4}$

$\frac{2x-y}{x+y} = \frac{2}{3}$

Cross multiplying yields

$6x-3y=2x+2y$

$4x=5y$

$\dfrac{x}{y}= \boxed{(\textbf{E}) \dfrac{5}{4}}$

1980 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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