Question

If $(x-9):(3x+6)$ is the duplicate ratio of $4:9$, find the value of $x$.

Answer 1

Given: $(x-9):(3x+6)$ is the duplicate ratio of $4:9$
$\Rightarrow \frac{x-9}{3x+6}={\left(\frac{4}{9}\right)}^2$
$\Rightarrow \frac{x-9}{3x+6}=\frac{16}{81}$
$\Rightarrow 81x-729=48x+96$
$\Rightarrow 81x-48x=96+729$
$\Rightarrow 33x=825$
$\Rightarrow x=\frac{825}{33}=25$