Question

Seth is deciding whether or not he should become a member of the YMCA to use their volleyball courts. The membership cost is $138. Members pay $7 to rent the volleyball courts.
Non-members can rent the court also, but they have to pay $9 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.
138 + 7×≥ 9×
138 ≥ 2x
69 ≥x
x ≤ 69
Seth would need to rent the court at most 69 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.

Answer 1

Seth is correct. Let's break down the reasoning behind his inequality:

Let's assume that Seth rents the court x times. If he becomes a member, he would pay a one-time membership cost of $138 and then pay $7 for each court rental.

So the cost for a member would be $138 + 7x.

If Seth chooses not to become a member, he would have to pay $9 each time he rents the court. So the cost for a non-member would be 9x.

Seth wants to find out when it becomes cheaper to be a member than a non-member. In other words, he wants to find the value of x for which the membership cost is less than the non-member cost.

Therefore, the inequality should be:
138 + 7x < 9x

Now let's solve this inequality:
138 < 9x - 7x
138 < 2x
69 < x

So, Seth is correct. He would need to rent the court at most 69 times for the membership to be cheaper than a non-membership.