To determine what the constant term [tex]\(-10\)[/tex] represents in the expression
[tex]\[ \frac{60r}{x+3} - 10 \][/tex]
where [tex]\(x\)[/tex] is the number of cheeseburgers sold, let's analyze each option one by one:
1. Option A: The constant -10 represents the cost of setting up the food stall even if no cheeseburgers were sold.
- This makes logical sense. The term [tex]\(-10\)[/tex] is subtracted from the revenue earned, which indicates it could represent a fixed cost associated with setting up the food stall. Even if no cheeseburgers are sold (i.e., [tex]\(x = 0\)[/tex]), there would still be a fixed setup cost of 10.
2. Option B: The constant -10 represents the maximum number of cheeseburgers sold by the food stall at the funfair.
- This interpretation is incorrect as the constant [tex]\(-10\)[/tex] does not provide information about the number of cheeseburgers sold. The number of cheeseburgers would be represented by [tex]\(x\)[/tex], not a constant term.
3. Option C: The constant -10 represents the total money earned by setting up the food stall.
- This is not accurate because the total money earned would be dependent on the number of cheeseburgers sold (i.e., [tex]\(x\)[/tex]). A constant term cannot represent a total money earned, which would fluctuate with sales.
4. Option D: The constant -10 represents the cost of each cheeseburger at the food stall.
- This is also incorrect. The cost of each cheeseburger would be a value that varies with the number of cheeseburgers sold and revenue generated, not a constant subtraction of 10 from the total.
Given these analyses, the correct interpretation is:
Option A: The constant -10 represents the cost of setting up the food stall even if no cheeseburgers were sold.
