Question

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

Find the value of $x$

Answer 1

Step : Find the value of $x$

We know, triplicate ratio is the cube of the given ratio.

$\therefore$ Triplicate ratio of $3:4\text{is}{3}^3:4^3$
$=27:64$

Given $;(3x-9):(5x+4)$ is the triplicate ratio of $3:4$

$\Rightarrow (3x-9):(5x+4)=27:64$

$\Rightarrow \frac{(3x-9)}{(5x+4)}=\frac{27}{64}$

$\Rightarrow 64(3x-9)=27(5x+4)$

$\Rightarrow 192x-576=135x+108$

$\Rightarrow 192x-135x=576+108$

$\Rightarrow 57x=684$

$\Rightarrow x=\frac{684}{57}$

$\therefore x=12$

Hence, the value of $x\text{is}12$