The cost of renting a kayak is [tex]$\$[/tex] 12[tex]$ for the first hour plus another $[/tex]\[tex]$ 5$[/tex] for each additional hour. Which of the following represents this situation, where [tex]$C$[/tex] is the total cost of renting a kayak for [tex]$h$[/tex] hours?

A. [tex]$C=5 h+12$[/tex]
B. [tex]$C=5(h-1)+12$[/tex]
C. [tex]$C=12 h+5$[/tex]
D. [tex]$C=17 h$[/tex]



Answer :

The question requires us to represent the total cost [tex]\( C \)[/tex] of renting a kayak for [tex]\( h \)[/tex] hours, based on the rates given: \[tex]$12 for the first hour and \$[/tex]5 for each additional hour.

Let's break down the problem step-by-step:

1. Understand the components of the cost:
- The cost for the first hour of renting the kayak is \[tex]$12. - For each additional hour after the first hour, the cost increases by \$[/tex]5.

2. Define the total cost [tex]\( C \)[/tex]:
- When [tex]\( h = 1 \)[/tex] (renting for only 1 hour), the total cost is simply the initial cost of \[tex]$12. - For \( h > 1 \), we need to account for the additional hours. The total number of additional hours beyond the first hour is \( h - 1 \). The cost for these additional hours is \( 5 \times (h - 1) \). 3. Construct the total cost expression: - The total cost \( C \) can be written as the sum of the initial cost for the first hour and the cost of the additional hours: \[ C = 12 + 5(h - 1) \] This equation captures the initial \$[/tex]12 charge and adds the additional cost for renting beyond the first hour.

4. Simplify the expression:
[tex]\[ C = 12 + 5(h - 1) = 12 + 5h - 5 = 5h + 7 \][/tex]

So, the total cost [tex]\( C \)[/tex] of renting a kayak for [tex]\( h \)[/tex] hours is represented by the equation:
[tex]\[ C = 5h + 7 \][/tex]

The answer corresponds to option B, which is:
[tex]\[ C = 5(h - 1) + 12 \][/tex]

Thus, the correct answer is [tex]\( \boxed{B} \)[/tex].