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# What is the ratio of $x$ to $y$ if: $\frac{10x-3y}{13x-2y} = \frac{3}{5}$? Express your answer as a common fraction.

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What is the ratio of $x$ to $y$ if: $\frac{10x-3y}{13x-2y} = \frac{3}{5}$? Express your answer as a common fraction.

Jan 18, 2021

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(10x - 3y)  / ( 13x - 2y)   =  3/5       cross-multiply

5(10x - 3y)  = 3(13x - 2y)   simplify

50x - 15y  =  39x - 6y     rearrange as

50x - 39x =  15y  - 6y

11x  =  9y

x / y  =  9 / 11

Jan 18, 2021