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.(1 point)

Answer 1

To represent the cost to play at the arcade based on the number of hours played, we can write the following piecewise function:

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

In this case:
- For the first hour (up to 1 hour), the cost \(C(h)\) is $15.
- After the first hour, for each additional hour, the cost increases by $5 for every hour beyond the first.

Now, let's calculate the cost to play for three hours:

1. For the first hour, it costs $15.
2. The additional time is \(3 - 1 = 2\) hours.
3. The cost for the additional hours is \(5 \times 2 = 10\).

So, the total cost for three hours is:

\[
C(3) = 15 + 10 = 25
\]

Thus, the cost to play for three hours is **$25.00**.