If (3x - 9) : (5x + 4) is the triplicate ratio of 3: 4, find the value of x.

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Solution

$\to \frac{(3 x - 9)}{(5 x + 4)} = \frac{3^{3}}{4^{3}}$
$\to \frac{3 (x - 3)}{(5 x + 4)} = \frac{27}{64}$
$\to \frac{(x - 3)}{(5 x + 4)} = \frac{9}{64}$
$\to 64 x - 192 = 45 x + 36$
$\to 19 x = 228$
$\to x = \frac{228}{19} = 12$
$\to x = 12$

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