If (x-9): (3x+6) is the triplicate ratio of 4:9. Find X.

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Solution

x-9 : 3x + 6 is the triplicate ratio of 4 : 9.
Hence $4^{3} : 9^{3} = x - 9 : 3 x + 6$
That is
$\frac{64}{729} = \frac{x - 9}{3 x + 6}$
Ie,
$192 x + 384 = 729 x - 6561$
$537 x = 6945$
$∴ x = \frac{6945}{537}$
Hence $x = \frac{2315}{179}$

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