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 based on the number of hours played (h), we can form the following piecewise equation:

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

Now, to calculate the cost for 3 hours:

Since \( h = 3 \) is greater than 1, we will use the second part of the piecewise equation:

\[ C(3) = 15 + 5 \times (3 - 1) \]

Calculating it step by step:

1. \( 3 - 1 = 2 \)
2. \( 5 \times 2 = 10 \)
3. \( C(3) = 15 + 10 = 25 \)

Thus, the cost to play for three hours is:

\[ C = 25.00 \]

So, the answer is \( C = \text{ } 25.00 \)

Answer 2

The bowling alley charges a flat rate for a lane, plus a fee per shoe rental. Use the equation C=15+3x to solve for the cost of getting a lane and four shoe rentals. Enter your answer, including cents.(1 point) $

Answer 3

In the equation \( C = 15 + 3x \):

• \( C \) is the total cost,
• \( 15 \) is the flat rate for the lane,
• \( 3 \) is the fee per shoe rental,
• \( x \) represents the number of shoe rentals.

To find the total cost for a lane and four shoe rentals (where \( x = 4 \)), we can substitute \( x \) into the equation:

\[ C = 15 + 3(4) \]

Now, calculate it step by step:

1. \( 3 \times 4 = 12 \)
2. \( C = 15 + 12 = 27 \)

Thus, the total cost for getting a lane and four shoe rentals is:

\[ C = 27.00 \]

The answer is \( C = \text{ } 27.00 \)