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)

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)

$ ___

GPT-4o mini · Answer

The cost to play at the arcade can be represented by the following piecewise equation:

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

To calculate the cost for three hours of play, we use the second part of the equation since $ h = 3 $ is greater than $ 1 $:

\[ C(3) = 15 + 5(3 - 1) \] \[ C(3) = 15 + 5(2) \] \[ C(3) = 15 + 10 \] \[ C(3) = 25 \]

Thus, the cost to play for three hours is:

\[ \boxed{25.00} \]