Creating Two-Variable Equations Practice

Question

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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 represent the cost to play at the arcade based on the number of hours played, we can create a piecewise equation. The cost \( C \) can be expressed as follows:

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

This equation shows that:

• For up to 1 hour of play, the cost is $15.00.
• For every additional hour played beyond the first hour, it costs $5.00.

Now, let's calculate the cost for 3 hours of play.

Since 3 hours is greater than 1, we will use the second part of our piecewise function:

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

So, the cost to play for three hours is \( C = 25.00 \).

The final answer is: \[ \text{Cost } C = $25.00 \]