If $x : y = 3 : 4$ , find $(4 x + 5 y) : (5 x - 2 y)$ .

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Solution

$\frac{x}{y} = \frac{3}{4} \Rightarrow \frac{4 x + 5 y}{5 x - 2 y} = \frac{4 (\frac{x}{y}) + 5}{5 (\frac{x}{y}) - 2} = \frac{(4 \times \frac{3}{4} + 5)}{(5 \times \frac{3}{4} - 2)} = \frac{(3 + 5)}{(\frac{7}{4})} = \frac{32}{7}$

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