Molly Dymond and Kathleen Taylor are considering the possibility of teaching swimming to kids during the summer. A local swim club opens its pool at noon each day, so its available to rent during the morning. The cost of renting the pool during the 10-week period for which Molly and Kathleen would need it is $1,700. The pool would also charge Molly and Kathleen an admission, towel service, and life guarding fee of $7 per pupil, and Molly and Kathleen estimate an additional $5 cost per student to hire several assistants. Molly and Kathleen plan to charge $75 per student for the 10-week swimming class.
A) How many pupils do Molly and Kathleen need to enroll in their class to break even?
B) If Molly and Kathleen want to make a profit of $5000 for the summer, how many pupils do they need to enroll?
C) Molly and Kathleen estimate that they might not be able to enroll more than 60 pupils. If they enroll this many pupils, how much would they need to charge per pupil in order to realize their profit goal of $5000

I am so confused with variable cost. Isn't it $12? And I have no clue about the problem C.

Okay, to start, the cost of the project. Let p be the number of pupils.

Total cost = 1 700 + 7p + 5p = 1 700 + 12p

Total revenue = 75p

A) If they break even, then

Total cost = Total revenue.

Solve for p

B) If they make 5 000 profit, then, there should be more revenue, meaning:

Total cost + Profit = Total revenue

Solve for p again.

C) Now, you know the number of pupils, which is 60, but the fee for each pupil is to be determined. Let the fee be denoted by f.

Total revenue = 60f

Total cost = 1 700 + 12(60)

The equation is still the same, apart some minor changes:

Total cost + Profit = Total revenue