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

Solution

$$\dfrac{m+n}{m+3n}=\dfrac{2}{3}$$
$$3m+3n=2m+6n$$
$$m=3n$$ (1)
$$\dfrac{60n^{2}}{3m^{2}+mn}=\dfrac{60n^{2}}{3(3n)^{2}+(3n)n}=\dfrac{60n^{2}}{27n^{2}+3n^{2}}=\dfrac{60n^{2}}{30n^{2}}=2$$
Hence the correct answer is 2.