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The following expression models the total money earned by setting up a food stall at a funfair, where [tex]x[/tex] represents the number of cheeseburgers sold:
[tex]\[
\frac{60x}{x+3} - 10
\][/tex]
What does the constant term in the above expression represent?

A. The constant -10 represents the cost of each cheeseburger at the food stall.
B. The constant -10 represents the total money earned by setting up the food stall.
C. The constant -10 represents the cost of setting up the food stall even if no cheeseburgers were sold.
D. The constant -10 represents the maximum number of cheeseburgers sold by the food stall at the funfair.



Answer :

GinnyAnswer
To understand what the constant term [tex]\(-10\)[/tex] in the given expression [tex]\(\frac{60x}{x+3} - 10\)[/tex] represents, let's analyze each part of the expression.

Consider the term [tex]\(\frac{60x}{x+3}\)[/tex]:
- The numerator [tex]\(60x\)[/tex] suggests that the revenue is directly proportional to the number of cheeseburgers [tex]\(x\)[/tex] sold.
- The denominator [tex]\(x+3\)[/tex] causes the revenue to be reduced as it is divided by [tex]\(3\)[/tex] plus the number of cheeseburgers sold, indicating some kind of diminishing returns or an adjustment factor.

Now, let's look at the constant term [tex]\(-10\)[/tex]:
- This term is subtracted from the overall revenue represented by [tex]\(\frac{60x}{x+3}\)[/tex].
- A constant subtracted from a revenue function typically represents a fixed cost that needs to be paid regardless of the number of cheeseburgers sold.

Given these observations, the constant term [tex]\(-10\)[/tex] makes the most sense as a fixed cost that is subtracted from the revenue generated by selling cheeseburgers.

Therefore, the correct interpretation is:

C. The constant -10 represents the cost of setting up the food stall even if no cheeseburgers were sold.

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