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 create a piecewise equation:

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

This equation states that for the first hour, the cost is $15. For each additional hour after the first, the cost is $5 for each additional hour played.

To calculate the cost for three hours, 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 would be $25.00.