Answer
a) The theater will lose 500 dollars, if no ticket is sold.
b) The theater will make no profit if 25 tickets are sold.
c) $P(100)$ represents the profit, in dollars, made by the theater if 100 tickets are sold.
Work Step by Step
(a) We have $P(0)=20(0)-500=-500$ dollars, which means that if no tickets are sold, the theater will lose 500 dollars.
(b) Setting $P(n)=0$ and solving, we get
$$
\begin{aligned}
20 n-500 & =0 \\
20 n & =500 \\
n & =25 .
\end{aligned}
$$
The theater will make no profit if 25 tickets are sold.
(c) $P(100)$ represents the profit, in dollars, made by the theater if 100 tickets are sold.
