Question

A fitness center is hosting a special promotion for group classes. The center can accommodate a maximum of 200 participants. The center is offering two types of classes: yoga (Y) and spin (S). Each yoga class requires 5 participants to run, while each spin class requires 10 participants

1. Create a two-variable linear inequality that represents the constraint of total number of participants. Clearly define your variables (5 points)



2. The center schedules 6 yoga classes and 8 spin classes. Using the inequality created in part 1 determine if this schedule meets the participant's capacity.

Answer 1

Let Y = number of yoga classes and S = number of spin classes.
Each yoga class needs 5 participants and each spin class needs 10 participants, and the center can hold at most 200 participants, so the constraint is

5Y + 10S ≤ 200.

For Y = 6 and S = 8: 5(6) + 10(8) = 30 + 80 = 110, and 110 ≤ 200.
So this schedule meets the capacity (it uses 110 participants, leaving room for 90 more).