If x : y = 3 : 4, find (3x + 4y) : (5x + 6y).

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Solution

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

Now, we have (3x + 4y) : (5x + 6y)
$= \frac{3 x + 4 y}{5 x + 6 y} = \frac{3 \times \frac{3 y}{4} + 4 y}{5 \times \frac{3 y}{4} + 6 y} = \frac{9 y + 16 y}{15 y + 24 y} = \frac{25 y}{39 y} = \frac{25}{39}$

= 25 : 39

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