Question

A camp manager needs to hire counselors, c, and counselors-in-training, or trainees, t, to staff summer camps. She will pay each counselor $16 per hour and each trainee $12 per hour. Answer questions 1-3 to help her decide how many of each she should hire to minimize her costs for staff.

Answer 1

Answer: The camp manager needs at least 40 staff members. Write an inequality that represents this situation.

Let c be the number of counselors and t be the number of trainees. Then the total number of staff members is c + t. Since the manager needs at least 40 staff members, we can write the inequality:

c + t ≥ 40

The camp manager has a budget of $1200 per day to spend on staff. Write an inequality that represents this situation.

Let H be the number of hours worked by all staff members combined. Then the total cost of staff per day is:

16c + 12t ≤ 1200

This inequality ensures that the total cost of staff does not exceed the budget of $1200 per day.

The camp manager wants to hire at least 4 counselors for every 5 trainees. Write an inequality that represents this situation.

Let c be the number of counselors and t be the number of trainees. Then the camp manager wants to satisfy the inequality:

c ≥ (4/5)t

This inequality ensures that there are at least 4 counselors for every 5 trainees, or equivalently, that the ratio of counselors to trainees is at least 4:5.

Explanation: