Question

Creating Two-Variable Equations Practice
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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 create an equation that represents the cost \( C \) based on the number of hours played \( h \), we can break it down as follows:

1. For the first hour, the cost is $15.00.
2. For each additional hour after the first hour, the cost increases by $5.00.

From these points, we can write the piecewise equation for the cost:

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

However, we can also write a single equation for \( h \geq 1 \):

\[
C(h) = 15 + 5(h - 1) = 15 + 5h - 5 = 5h + 10
\]

Now, to calculate the cost for three hours (\( h = 3 \)):

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

Therefore, the cost to play for three hours is:

\[
\text{Cost } = C = \mathbf{25.00}
\]

So the answer for \( C \) is:

\[
\boxed{25.00}
\]