Question

Evan works full shifts at a community center and at a gym. His shifts at the community center are 5 hours and his shifts at the gym are 3 hours. He can work a shifts at the community center and y shifts at the gym for up to 30 total hours each week. He can only work full shifts.

Part A
Which system of inequalities represents all possible numbers of shifts that Evan can work at the community center and at the gym?

Answer 1

The system of inequalities representing the number of shifts Evan can work at the community center and the gym without exceeding a total of 30 hours per week is 5a + 3y ≤ 30, a ≥ 0, and y ≥ 0.

Step-by-step explanation:

The student's question involves creating a system of inequalities to represent the possible number of shifts Evan can work at two locations given a maximum number of hours he can work each week. As Evan works 5-hour shifts at the community center and 3-hour shifts at the gym, we use variables a to represent the number of shifts at the community center and y for the gym. The total working hours must not exceed 30 hours per week, and he can only work full shifts.

The system of inequalities that represents this scenario is:

5a + 3y ≤ 30 (for the total hours worked),

a ≥ 0 (he can't work negative shifts at the community center),

y ≥ 0 (he can't work negative shifts at the gym).

This system allows us to determine all possible combinations of shifts at the community center and the gym that will not exceed 30 hours in total per week.