Sandra sells necklaces at a school craft fair. She uses the equation P= 7.5n - (2.25n + 15) to determine her total profit at the fair. Based on this equation, how much does she charge for each necklace?A. $2.25B. $7.50C. $15.00D. $17.25This question has been posted with answers...but I am not in understanding. Would someone mind explaining WHY the answer is $7.50? Why wouldn't it be $2.25?

Accepted Solution

The way you find profit is to subtract the revenue and the cost
Profit = Revenue - Cost
The revenue is the amount of money coming in, the cost is the amount of money going out. The goal of course is to have the revenue larger than the cost so that the profit is positive. 

So the equation given is
P = 7.5n - (2.25n+15)
and its in the form
P = R - C
R = 7.5n is the revenue equation
C = 2.25n+15 is the cost equation

Focus on the revenue equation
R = 7.5n
which is the same as 
R = 7.50*n

This tells us that Sandra pulls in a total of 7.50*n dollars where n is some positive whole number. It represents the number of necklaces sold. For example, if she sold n = 10 necklaces, then
R = 7.50*n
R = 7.50*10
R = 750
meaning that Sandra has made $750 in revenue

As you can see above, the revenue is computed by multiplying the price per necklace ($7.50) by the number of necklaces sold (n) to get R = 7.50*n

So that's why the answer is $7.50

Note: The 2.25 is part of the cost equation. This is known as the variable cost. It is the cost to make one necklace ignoring the fixed cost (eg: rent). The variable cost often doesn't stay the same, but algebra textbooks often simplify this aspect.