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# Help

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If the ratio of  2x - y to x + y is 2 to 3, what is the ratio of x  to y ? Express your answer as a common fraction.

Logic  Aug 17, 2018
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2x + 2y =6x -3y, solve for x/y
2x - 6x = -3y -2y
-4x = -5y
-4x / -5y =1
x/y =5/4

Guest Aug 17, 2018
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As follows:

$$\text{Start as follows: }\frac{2x-y}{x+y}=\frac{2}{3}\\ \text{ Then multiply both sides by }3(x+y)\\ 3(2x-y)=2(x+y)\text{ or }6x-3y=2x+2y\\\text{Collect like terms together: }4x=5y\\\text{Divide both sides by }4y\\\frac{x}{y}=\frac{5}{4}$$

Alan  Aug 17, 2018