Seth is deciding whether or not he should become a member of the YMCA to use their volleyball courts. The membership costs $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 to be cheaper? than a non-member?

Question

Seth is deciding whether or not he should become a member of the YMCA to use their volleyball courts. The membership costs $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 to be cheaper? than a non-member?

138+7x greater or equal to 9x
138 greater or equal to 2x
69 greater or equal to x
x less or equal to 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 incorrect explain why by setting up the correct inequality and solve it.

Answer 1

Seth is incorrect in his reasoning.

Let's set up the correct inequality and solve it:

Let's assume Seth wants to rent the court "n" times.

For a non-member, the cost of renting the court "n" times would be 9n dollars.

For a member, the cost of renting the court this many times would be the sum of the membership fee and the rental fee, which is 138 + 7n dollars.

Now let's set up the inequality:

138 + 7n < 9n

Subtracting 7n from both sides, we get:

138 < 2n

Dividing both sides by 2, we get:

69 < n

So, the correct inequality is n > 69.

Therefore, Seth would need to rent the court more than 69 times for the membership to be cheaper than a non-membership.

Answer 2

Seth is correct in his calculation that he would need to rent the court at most 69 times for the membership to be cheaper than a non-membership.

The correct inequality to set up is:
138 + 7x < 9x

Now we can solve it:
138 < 9x - 7x
138 < 2x
138/2 < x
69 < x

This means that Seth would need to rent the court more than 69 times for the non-membership option to be cheaper. Therefore, Seth is correct in his conclusion.

Answer 3

Seth is partially correct with his inequality setup, but there is a mistake in his calculation. Let's break it down and explain it step by step:

1. Seth correctly identified that the total cost for a member is $138 (membership fee) plus $7 per court rental.
So, the cost for a member can be represented as 138 + 7x, where x is the number of court rentals.

2. Seth also correctly identified that the total cost for a non-member is $9 per court rental.
So, the cost for a non-member can be represented as 9x.

3. Now, Seth wants to find out the number of court rentals at which it would be cheaper to become a member than to rent as a non-member. To express this mathematically, we set up the following inequality:
138 + 7x ≤ 9x
The left-hand side (LHS) represents the total cost for a member, and the right-hand side (RHS) represents the total cost for a non-member.

4. To simplify the inequality, we need to isolate the variable. Let's subtract 7x from both sides of the equation:
138 ≤ 9x - 7x
Simplifying the RHS yields:
138 ≤ 2x

5. Now, to isolate x, we divide both sides of the equation by 2:
138/2 ≤ 2x/2
69 ≤ x

So, Seth's initial calculation was correct in terms of the direction of the inequality, but he made a mistake in the calculation. The correct answer is that Seth would need to rent the court at most 69 times for the membership to be cheaper than renting as a non-member.

Therefore, Seth's conclusion is correct, and he would need to rent the court at most 69 times for membership to be cheaper than renting as a non-member.