Question

If $\frac{m+n}{m+3n}=\frac{2}{3}$, find: $\frac{60n^2}{3m^2+mn}$.

Answer 1

$\frac{m+n}{m+3n}=\frac{2}{3}$

$3m+3n=2m+6n$

$m=3n$ (1)

$\frac{60n^2}{3m^2+mn}=\frac{60n^2}{3(3n{)}^2+(3n)n}=\frac{60n^2}{27n^2+3n^2}=\frac{60n^2}{30n^2}=2$

Hence the correct answer is 2.