1. **Problem statement:** We need to create a linear inequality representing the total number of participants for yoga and spin classes, given the constraints. Define variables: - Let $Y$ = number of yoga classes - Let $S$ = number of spin classes Each yoga class requires 5 participants, so total yoga participants = $5Y$. Each spin class requires 10 participants, so total spin participants = $10S$. The center can accommodate a maximum of 200 participants, so the total participants must be less than or equal to 200. 2. **Formulating the inequality:** $$5Y + 10S \leq 200$$ This inequality ensures the total number of participants from yoga and spin classes does not exceed the center's capacity. 3. **Checking the schedule:** Given $Y = 6$ yoga classes and $S = 8$ spin classes, substitute into the inequality: $$5(6) + 10(8) = 30 + 80 = 110$$ Since $110 \leq 200$, the schedule meets the participant capacity. **Final answer:** - Inequality: $$5Y + 10S \leq 200$$ - Schedule check: $$5(6) + 10(8) = 110 \leq 200$$, so the schedule is valid.