To find the correct equation representing the cost function for the bookstore, we need to understand the components that contribute to the total cost.
1. Fixed Daily Cost: This is the constant cost the bookstore incurs every day, regardless of how many books are sold. According to the problem, this fixed cost is [tex]$75$[/tex].
2. Variable Cost Per Book: This is the additional cost incurred for each book sold. The problem states that the bookstore spends [tex]$10 for each book it sells. So, if $[/tex]n[tex]$ books are sold, the total variable cost would be $[/tex]10n$.
By combining these two components:
- The total cost of running the bookstore is equal to the sum of the fixed daily cost and the variable cost per book sold.
Thus, we can express the cost function [tex]\( C \)[/tex] as:
[tex]\[ C = \text{Fixed Cost} + \text{Variable Cost Per Book} \times n \][/tex]
Substituting in the given values:
[tex]\[ C = 75 + 10 \times n \][/tex]
[tex]\[ C = 75 + 10n \][/tex]
[tex]\[ C = 10n + 75 \][/tex]
Now, we will compare this equation with the given options:
- A. [tex]\( C = 75n + 15 \)[/tex]
- B. [tex]\( C = 75n + 10 \)[/tex]
- C. [tex]\( C = 15n + 75 \)[/tex]
- D. [tex]\( C = 10n + 75 \)[/tex]
The equation that correctly represents the cost function based on the given problem is:
D. [tex]\( C = 10n + 75 \)[/tex]
So the correct answer is:
[tex]\[ \boxed{D} \][/tex]
