Seth is deciding whether or not he should become a member of the YMCA to use their volleyball courtsThe membership cost is $138 Members pay $7 to rent the volleyball courtsNon-members can rent the court also, but they have to pay $9 each timehow 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 + 7x => 9x
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.
Seth is correct. By renting the court as a member, Seth would have to pay $7 per rental. On the other hand, as a non-member, he would have to pay $9 per rental.
Let's calculate the costs for Seth to rent the court 69 times:
- As a member: 7 * 69 = $483
- As a non-member: 9 * 69 = $621
As we can see, the cost of the membership ($138) plus the cost of rentals as a member ($483) is cheaper than renting the court as a non-member ($621). Therefore, Seth would need to rent the court at most 69 times for the membership to be cheaper than being a non-member.
Seth is not correct in the way he set up the inequality. Let's break down the problem again to set up the correct inequality.
For Seth to decide if it is cheaper to become a member or not, we need to compare the total cost for renting the courts as a member versus as a non-member.
As a member, Seth would pay a membership cost of $138 upfront and then $7 for each time he rents the volleyball court.
As a non-member, Seth would pay $9 each time he rents the court, with no additional membership cost.
Let's call the number of times Seth rents the court "x". So, the total cost as a member would be 138 + 7x, and the total cost as a non-member would be 9x.
Now, to find out when it would be cheaper to become a member, we set up the following inequality:
138 + 7x < 9x
To solve this inequality, we can rearrange it as:
138 < 9x - 7x
138 < 2x
Dividing both sides of the inequality by 2, we get:
69 < x
So, the correct inequality is x > 69.
Therefore, Seth would need to rent the court more than 69 times for the membership to be cheaper than being a non-member.
Seth is not correct in setting up the inequality. The correct inequality should take into account the difference between the cost of renting the court as a member and as a non-member.
Let's analyze the situation:
As a member, Seth would pay a membership cost of $138 and $7 per court rental. So the total cost of renting the court x number of times as a member would be 138 + 7x.
As a non-member, Seth would pay $9 per court rental, without any membership cost. So the total cost of renting the court x number of times as a non-member would be 9x.
Now, let's set up the correct inequality:
138 + 7x < 9x
We want to find the number of times Seth needs to rent the court for it to be cheaper to be a member. So, we need to solve this inequality for x.
Subtracting 7x from both sides:
138 < 9x - 7x
Simplifying:
138 < 2x
Now, divide both sides by 2 to isolate x:
69 < x
This means that Seth would need to rent the court more than 69 times for the membership to be cheaper than being a non-member.
Therefore, Seth's initial answer was incorrect. The correct answer is that Seth would need to rent the court more than 69 times for the membership to be cheaper than a non-membership.