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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.



How would I go about solving this problem

 Mar 27, 2019


First, I'd multiply both sides by 5 and then multiply both sides by (13x - 2y)

Sometimes this is called cross-multiplying. 


the result of cross-multiplying is        (5)(10x - 3y) = (3)(13x -2y)


multiply it out                                       50x -15y = 39x - 6y 


put like unknowns together                  50x - 39x = 15y - 6y


combine/subtract terms                            11x = 9y


divide both sides by y                                11x/y = 9


divide both sides by 11                                x/y = 9/11     the ratio of x to y is 9 to 11

 Mar 27, 2019

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