phrase the answer in a way a 12 yr old would

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)

Answer 1

Sure! Let’s break this down into simpler parts.

1. Defining the variables:

   • Let's call Y the number of yoga classes.
   • Let's call S the number of spin classes.

   Each yoga class needs 5 people, and each spin class needs 10 people. The total number of participants can’t be more than 200. So, we can write the inequality like this:

   5Y + 10S ≤ 200

   This means if you add up all the people in yoga classes and spin classes, it shouldn’t be more than 200.

2. Checking the schedule: The center has 6 yoga classes and 8 spin classes scheduled.

   • For the yoga classes:
     \( 5 \times 6 = 30 \) participants
   • For the spin classes:
     \( 10 \times 8 = 80 \) participants

   Now, let's add those together: \( 30 + 80 = 110 \)

   Since 110 is less than 200, this schedule works! So, yes, it meets the participant's capacity.