If the ratio of 2x-y to x+y is 23, what is the ratio of x to y?

1980 AMC 12 Problem 3

Attempt Problem 3 of the 1980 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1980 AMC 12 solutions, or check the answer key.

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If the ratio of

2x-y

x+y

\frac23,

what is the ratio of

x

y?

\frac15

\frac45

1

\frac65

\frac54

Write the stated ratio as an equation of two fractions

Cross-multiply and collect the

x

-terms and

y

-terms separately

The condition gives

\frac{2x-y}{x+y}=\frac23.

Thus

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

4x=5y

and

\frac{x}{y}=\frac{5}{4}.

Therefore, the correct answer is E.