Hannah Byers 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 it is available to rent during the morning. The cost of renting the pool during the 10-week period for which Hannah and Kathleen would need it is $1,700. The pool would also charge Hannah and Kathleen an admission, towel service, and life guarding fee of $7 per student, and Hannah and Kathleen estimate an additional $5 cost per student to hire several assistants. Hannah and Kathleen plan to charge $75 per student for the 10-week swimming class.

a. How many students do Hannah and Kathleen need to enroll in their class to break-even?

b. If Hannah and Kathleen want to make a profit of $5000 for the summer, how many students do they need to enroll?

c. Hannah and Kathleen estimate that they might not be able to enroll more than 60 students. If they enroll this many students, how much would they need to charge per student in order to realize their profit goal of $5000?