If $x : y = 3 : 5$ find ratio $3 x + 4 y : 8 x + 5 y$

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Solution

Given that x : y = 3 : 5
(0r) $\frac{x}{y} = \frac{3}{5}$
Let us assume that x = 3k and y = 5k
$\frac{3 x + 4 y}{8 x + 5 y} = \frac{3 (3 k) + 4 (5 k)}{8 (3 k) + 5 (5 k)}$
$\frac{9 k + 20 k}{24 k + 25 k} = \frac{29 k}{49 k} = \frac{29}{49}$
Hence 3x + 4y : 8x + 5y = 29 : 49

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