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.

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.

GPT-4o mini · Answer

To represent the cost $ C $ based on the number of hours played $ h $, we can set up the following piecewise equation: $$ C(h) = \begin{cases} 15 & \text{if } 0 < h \leq 1 \ 15 + 5(h - 1) & \text{if } h > 1 \end{cases} $$ This means: - If you play for up to 1 hour, the cost is $15. - If you play for more than 1 hour, the cost starts at $15 for the first hour and then adds $5 for each additional hour after the first. Now, to calculate the cost to play for 3 hours ($ h = 3 $), we use the second part of our equation since $ 3 > 1 $: $$ C(3) = 15 + 5(3 - 1) $$ Calculating it step-by-step: 1. Calculate $ 3 - 1 = 2 $. 2. Multiply $ 2 $ by $ 5 $: $ 5 \times 2 = 10 $. 3. Add $ 10 $ to $ 15 $: $ 15 + 10 = 25 $. Thus, the cost to play for 3 hours is: $$ C(3) = 25.00 $$ So, the final answer is $ C = 25.00 $.