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 to play, \( C \), based on the number of hours played, \( h \), we can break it down into two cases:

1. **For the first hour (0 < h ≤ 1)**: The cost is $15.00.
2. **For additional hours (h > 1)**: The cost for the first hour is $15.00, and each additional hour costs $5.00.

We can express this with the following piecewise function:

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

Now, let's calculate the cost for three hours of playtime:

Since \( h = 3 \) which is greater than 1, we use the second part of the piecewise function:

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

Calculating inside the parentheses first:

\[
C(3) = 15 + 5(2)
\]

Now, multiply:

\[
C(3) = 15 + 10
\]

Finally, add these together:

\[
C(3) = 25
\]

Thus, the total cost to play for three hours is:

\[
C = 25.00
\]