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 create an equation that represents the cost to play, C, based on the number of hours played, h, we can set it up as follows:

- For the first hour (h = 1), the cost is $15.00.
- For each additional hour (h > 1), the cost is $5.00 per hour.

Thus, the equation for C can be defined as:

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

Now, let's use this equation to calculate the cost for three hours (h = 3):

Since 3 > 1, we use the second part of the equation:

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

Calculating the values:

\[
C = 15 + 5(2)
\]
\[
C = 15 + 10
\]
\[
C = 25
\]

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