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

Cross multiplying gets 6x-3y=2x+2y4x=5y xy=54 54

smc

algebra intermediate

Problem

If the ratio of

2 x - y

x + y

\frac{2}{3}

, what is the ratio of

x

y

(A)

\frac{1}{5}

(B)

\frac{4}{5}

(C)

1

(D)

\frac{6}{5}

(E)

\frac{5}{4}

Solution

Cross multiplying gets

6 x - 3 y = 2 x + 2 y 4 x = 5 y \frac{x}{y} = \frac{5}{4} \frac{5}{4}

Final answer