To determine the correct equation that models the relationship between the total cost to rent skis, [tex]\( c \)[/tex], and the length of the rental in days, [tex]\( d \)[/tex], we need to consider the given pricing structure:
1. There is a fixed base cost of \[tex]$15.
2. There is an additional cost of \$[/tex]20 per day.
We will build our equation step-by-step:
1. Base Cost: The rental has a base cost of \[tex]$15, regardless of the number of days. This means that no matter how many days you rent the skis, you will always have to pay this fixed amount.
- Therefore, this contributes \( 15 \) to the total cost \( c \).
2. Cost per Day: For each day you rent the skis, you pay an additional \$[/tex]20. So if you rent the skis for [tex]\( d \)[/tex] days, the total cost for the days would be [tex]\( 20d \)[/tex].
- This means we have a term [tex]\( 20d \)[/tex] in our total cost calculation.
By combining these two components (the fixed base cost and the variable daily cost), we form the equation:
[tex]\[ c = 20d + 15 \][/tex]
Thus, the equation that models the relationship between the total cost to rent skis, [tex]\( c \)[/tex], and the length of the rental in days, [tex]\( d \)[/tex], is:
[tex]\[ c = 20d + 15 \][/tex]
This matches the third option given:
[tex]\[ \boxed{c = 20d + 15} \][/tex]
