Answer
(a) $C=22.75t+36,500$
(b) $R=30t$
(c) $t=5034.48$ hours
Work Step by Step
Let $t$ be the hours of operation of the equipment.
(a) We know that it costs \$9.25 an hour for fuel and maintenance. This can be represented as $9.25t$. We know also that the equipment operator is paid \$13.50 an hour. This can be represented as $13.5t$. Finally, the equipment was purchased for \$36,500. Adding all of these costs together, we get
\begin{align*}
C&=9.25t+13.5t+36,500\\
&=22.75t+36,500 &&\text{(combine like terms)}
\end{align*}
(b) We know the customer is charged \$30 per hour that the machine is in use. This can be represented as $30t$. Thus, $R=30t$.
(c) The break-even point is found by finding $t$ when $R=C$. So, we have
\begin{align*}
R&=C\\
30t&=22.75t+36,500 &&\text{(substitute equations)}\\
7.25t&=36,500 &&\text{(subtract $22.75t$)}\\
t&=5034.48 &&\text{(divide by 7.25)}\\
\end{align*}
