If $(4 x + 3 y) : (3 x + 5 y) = 6 : 7,$ find $x : y$

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Solution

$7 \times (4 x + 3 y) = 6 \times (3 x + 5 y)$
$28 x + 21 y = 18 x + 30 y$
$28 x - 18 x = 30 y - 21 y$
$10 x = 9 y$
$\frac{x}{y} = \frac{9}{10}$
$∴ x : y = 9 : 10$

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