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

Question

, 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:

\[ C = 25.00 \]