Question

If $\frac{5}{2y+5}=\frac{4}{y+2}$, then $y=\frac{-10}{x}$. Find $x$.

Answer 1

Given, $\frac{5}{2y+5}=\frac{4}{y+2}$

$\Rightarrow 5(y+2)=4(2y+5)$ ...[Cross-multiplying the denominators]

$\Rightarrow 5y+10=8y+20$ ...[By Distribution Law].

Transposing $y$ terms to one side, we get,

$\Rightarrow 5y-8y=20-10$

$\Rightarrow -3y=10$

$\Rightarrow y=\frac{-10}{3}$.

But, given, $y=\frac{-10}{x}$.

Comparing, we get, $x=3$.