Question

A local arcade charges $15.00 for unlimited play time for the first hour, then $5.00 per additional hour. On a piece of paper, write an equation that represents the cost to play, C , based on the number of hours played, h. Then use the equation to calculate how much it would cost to play for three hours. Enter your answer for C , including cents.

Answer 1

To represent the cost \( C \) based on the number of hours played \( h \), we can set up the following piecewise equation:

\[
C(h) =
\begin{cases}
15 & \text{if } 0 < h \leq 1 \\
15 + 5(h - 1) & \text{if } h > 1
\end{cases}
\]

This means:
- If you play for up to 1 hour, the cost is $15.
- If you play for more than 1 hour, the cost starts at $15 for the first hour and then adds $5 for each additional hour after the first.

Now, to calculate the cost to play for 3 hours (\( h = 3 \)), we use the second part of our equation since \( 3 > 1 \):

\[
C(3) = 15 + 5(3 - 1)
\]

Calculating it step-by-step:

1. Calculate \( 3 - 1 = 2 \).
2. Multiply \( 2 \) by \( 5 \): \( 5 \times 2 = 10 \).
3. Add \( 10 \) to \( 15 \): \( 15 + 10 = 25 \).

Thus, the cost to play for 3 hours is:

\[
C(3) = 25.00
\]

So, the final answer is \( C = 25.00 \).