SAT Mathematics Practice Test 2

The amount of money the performer earns is directly proportional to the number of people who attend the performance. Thus, by the definition of direct proportionality, $\mathit{M}=\mathit{k}\mathit{P}$, where M is the amount of money the performer earns, in dollars, $\mathit{P}$ is the number of people who attend the performance, and $\mathit{k}$ is a constant. Since the performer earns $120$ when 8 people attend the performance, one can substitute $120$ for $\mathit{M}$ and $8$ for $\mathit{P}$, giving $120=8\mathit{k}$. Hence, $\mathit{k}=15$,and the relationship between the number of people who attend the performance and the amount of money, in dollars, the performer earns is $\mathit{M}=15\mathit{P}$. Therefore, when 20 people attend the performance, the performer earns $15\left(20\right)=300$ dollars.Choices A, B, and D are incorrect and may result from either misconceptions about proportional relationships or computational errors.