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Question

If $x : y = 4 : 7,$ find the value of ( $3 x + 2 y$ ) : ( $5 x + y$ )

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Solution

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Given, $x : y = 4 : 7 ⟹ \frac{x}{y} = \frac{4}{7}$
$\frac{3 x + 2 y}{5 x + y} = \frac{3 (\frac{x}{y}) + 2}{5 (\frac{x}{y}) + 1} = \frac{\frac{12}{7} + 2}{\frac{20}{7} + 1} = \frac{26}{27}$

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