Question

Find the value of $x$ if

$\left(iii\right)$ $(3x-7):(4x+3)$ is the sub-triplicate ratio of $8:27$

Answer 1

Step: Find the value of $x$

Cube root of given ratio is the sub-triplicate ratio

$\therefore$ Sub-triplicate ratio $8:27\text{is}\sqrt[3]{38}:\sqrt[3]{327}$

$=\sqrt[3]{32^3}:\sqrt[3]{33^3}$

$=2:3$

Now, $\frac{3x-7}{4x+3}=\frac{2}{3}$

$\Rightarrow 3(3x-7)=2(4x+3)\left[\text{cross product}\right]$

$\Rightarrow 9x-21=8x+6$

$\Rightarrow 9x-8x=21+6$

$\Rightarrow x=27$

Hence, the value of $x$ is $27$.