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. (2 points)

(7 points)

Answer 1

1. **Defining Variables and Creating the Inequality:**

Let:
- \( Y \) = number of yoga classes
- \( S \) = number of spin classes

Each yoga class requires 5 participants, and each spin class requires 10 participants. The total number of participants must not exceed 200.

The inequality representing the total number of participants is:
\[
5Y + 10S \leq 200
\]

2. **Checking the Scheduled Classes Against the Inequality:**

The center schedules 6 yoga classes and 8 spin classes. We can substitute these values into the inequality to check if the participant capacity is met.

Substituting \( Y = 6 \) and \( S = 8 \):
\[
5(6) + 10(8) \leq 200
\]
\[
30 + 80 \leq 200
\]
\[
110 \leq 200
\]

Thus, the inequality holds true. The scheduled classes do meet the participant's capacity.