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)

give a short answer and use simple terms

Answer 1

1. **Variables Definition:**
- Let \( Y \) be the number of yoga classes.
- Let \( S \) be the number of spin classes.

**Inequality:**
The number of participants can be represented by the inequality:
\[
5Y + 10S \leq 200
\]

2. **Calculation for the Schedule:**
With 6 yoga classes and 8 spin classes, we can substitute \( Y = 6 \) and \( S = 8 \) into the inequality:
\[
5(6) + 10(8) = 30 + 80 = 110
\]

Since \( 110 \leq 200 \), the schedule meets the participant's capacity.