Problem: If the ratio of 2x−y2 x-y2x−y to x+yx+yx+y is 23\dfrac{2}{3}32, what is the ratio of xxx to y?y?y?
Answer Choices:
A. 15\dfrac{1}{5}51
B. 45\dfrac{4}{5}54
C. 111
D. 65\dfrac{6}{5}56
E. 54\dfrac{5}{4}45
Solution:
If 2x−yx+y=23\dfrac{2 x-y}{x+y}=\dfrac{2}{3}x+y2x−y=32, then
6x−3y=2x+2y4x=5yxy=54.\begin{aligned} 6 x-3 y & =2 x+2 y \\ 4 x & =5 y \\ \dfrac{x}{y} & =\dfrac{5}{4} . \end{aligned} 6x−3y4xyx=2x+2y=5y=45.