SAT math problem about solute and solution

Question

There are two solutions $P$ and $Q$. There are $50 g$ of $P$, which has $30\%$ benzene by mass, and $200 g$ of $Q$, which has $70\%$ benzene by mass. If $20 g$ of solution $P$ is added to $20 g$ of solution $Q$, what is the percent of benzene by mass in the resulting mixture?

Answer 1

$50$ grams of solution P has $30\%$ benzene by mass means in $50$ gm of solution P , benzene is $15$ gm. So $20$ gm of P will contain $15*\frac{20}{50}=6$ gm of benzene.

Similarly , $200$ gm of solution Q has $140$ gm of benzene . So , $20$ gm of Q will contain $14$ gm benzene .

In resulting solution , $20$ gm of benzene is present .

Percentage of benzene $=\frac{20}{40}*100\%=50\%$

Answer 2

Determine the mass of the final solution: $$(20 grams)+(20 grams)=40 grams$$

Determine the mass of benzene in the final solution: $$0.3*(20 grams)+0.7*(20 grams)=20 grams$$

Take the ratio of the two: $$\frac{20 grams}{40 grams}=50\%$$