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)

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.