Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.8 Junior Find the answer

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

Pick one

Solution

Cross multiplying gets
$6x-3y=2x+2y\\4x=5y\\ \dfrac{x}{y}=\dfrac{5}{4}\\ \boxed{(E)}$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.