If x : y = 3 : 4, find the ratio of 7x - 4y : 3x + y.

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Solution

Given that $x : y = 3 : 4$
$\Rightarrow \frac{x}{y} = \frac{3}{4}$

$\Rightarrow \frac{x}{3} = \frac{y}{4}$

Let the above ratio be equal to $k$
$\Rightarrow x = 3 k, y = 4 k$
The ratio of $(7 x - 4 y) : (3 x + y) = (21 k - 16 k) : (9 k + 4 k) = 5 k : 13 k = 5 : 13$

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