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Clever Algebraic Manipulations

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Given that $$\frac{a}{25-a}+\frac{b}{65-b}+\frac{c}{60-c}=7$$, evaluate $$\frac{5}{25-a}+\frac{13}{65-b}+\frac{12}{60-c}$$.

Sep 6, 2018

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Notice that 25 = 5*5,  65 = 13*5,  60 = 12*5.  One simple way is then as follows:

Other choices are possible for a, b and c, but they all lead to the same final result.

Sep 7, 2018