Seth is deciding whether or not he should become a member of the YMCA to use their volleyball courts. The membership cost is $154. Members pay $5 to rent the volleyball courts. Non-members can rent the court also, but they have to pay $12 each time. how many times would Seth need to rent the court in order for it be cheaper to be a member than a non-member?
Seth set up an Inequality to answer this question. 154 + 5x ≥ 12x
154 ≥ 7x
22≥ x
x ≤ 22
Seth would need to rent the court at most 22 times for the membership to be cheaper than a non membership
Explain if Seth is correct. If he is not correct, explain why by setting up the correct inequality and solve it
Yes, Seth is correct. The inequality 154 + 5x ≥ 12x represents the cost for Seth as a member (where he pays the membership fee of $154 and then $5 for each court rental) and the cost for Seth as a non-member (where he pays $12 for each court rental without a membership).
To determine when it would be cheaper for Seth to be a member, we need to find the value of x (the number of court rentals) that makes the cost for Seth as a member less than the cost for Seth as a non-member.
Solving the inequality 154 + 5x ≥ 12x:
154 ≥ 7x
22 ≥ x
This means that Seth would need to rent the court at most 22 times for the membership to be cheaper than being a non-member. If he rents the court 22 times or less, he will pay more as a non-member ($12 per rental) compared to being a member ($5 per rental after paying the $154 membership fee).