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 break down the information given in the problem:
1. Fixed Cost: There is a fixed cost of \[tex]$15 for renting the skis. This cost is independent of the number of days the skis are rented.
2. Variable Cost: There is an additional variable cost of \$[/tex]20 per day. This means that for each day the skis are rented, \[tex]$20 is added to the total cost.
To find the total cost \( c \) for renting the skis for \( d \) days, we can use the following steps:
- Start with the fixed cost, which is \$[/tex]15.
- Add the variable cost, which is \$20 multiplied by the number of days [tex]\( d \)[/tex].
The relationship can be expressed as:
[tex]\[ c = \text{fixed cost} + (\text{variable cost per day} \times \text{number of days}) \][/tex]
Translating this into a mathematical equation:
[tex]\[ c = 15 + 20d \][/tex]
Now, let's review the given multiple-choice answers:
1. [tex]\( c = (15 + 20)d \)[/tex] - This expression incorrectly adds the fixed cost and variable cost per day together before multiplying by the number of days. This is not correct.
2. [tex]\( c = 15d + 20 \)[/tex] - This expression incorrectly multiplies the fixed cost by the number of days and adds the variable cost incorrectly. This is not correct.
3. [tex]\( c = 20d + 15 \)[/tex] - This expression correctly multiplies the variable cost per day by the number of days and then adds the fixed cost. This is the correct equation.
4. [tex]\( c = (15 + d)20 \)[/tex] - This expression incorrectly adds the fixed cost and the number of days together and then multiplies by the variable cost per day. This is not correct.
Thus, 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], is:
[tex]\[ c = 20d + 15 \][/tex]
Therefore, the correct answer is:
[tex]\[ c = 20d + 15 \][/tex]
The corresponding choice from the options provided is:
[tex]\[ \boxed{c = 20d + 15} \][/tex]
