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

Question

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: $$5Y+10S\le 200$$

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 $S=8$: $$5(6)+10(8)\le 200$$ $$30+80\le 200$$ $$110\le 200$$

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