Seth is deciding whether or not he should become a member of the YMCA to use their volleyball courtsThe membership cost is $154Members pay $5 to rent the volleyball courtsNon-members can rent the court also, but they have to pay $12.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. 154+ 5x 2 12x
154 27 x
222 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 correctexplain why by setting up the correct inequality and solve it
Seth is incorrect in his setup of the inequality. Let's correct it.
Let's assume that Seth rents the court x number of times.
For a membership:
Total cost = Membership cost + Court rental cost
Total cost = $154 + $5x
For non-members:
Total cost = Court rental cost
Total cost = $12x
To determine when it is cheaper to be a member, we need to find the point at which the total cost for a membership is less than the total cost for a non-membership.
Therefore, we need to set up the following inequality:
154 + 5x < 12x
Now, let's solve this inequality to find the maximum value of x that satisfies it:
154 < 12x - 5x
154 < 7x
154/7 < x
22 < x
The correct inequality is x > 22.
So, Seth would need to rent the court more than 22 times for the membership to be cheaper than a non-membership.
Seth is not correct in his inequality setup.
To determine when it would be cheaper for Seth to be a member rather than a non-member, we need to compare the costs of renting the court as a member and as a non-member.
As a member, Seth would pay a membership cost of $154, plus $5 each time he rents the court. This can be represented as: 154 + 5x.
As a non-member, Seth would pay $12 each time he rents the court, without any membership cost. This can be represented as: 12x.
To find out when it would be cheaper for Seth to be a member, we need to set up an inequality:
154 + 5x < 12x
Simplifying the inequality, we get:
154 < 7x
Dividing both sides of the inequality by 7, we get:
22 < x
Therefore, Seth would need to rent the court more than 22 times for the membership to be cheaper than a non-membership.
Seth's inequality is not correct. Let me explain the correct process to set up the inequality and solve it.
To determine how many times Seth would need to rent the court for the membership to be cheaper than being a non-member, we need to compare the total cost of renting the court as a non-member with the cost of being a member.
Let's assume Seth rents the court "x" times as a non-member. The total cost of renting the court as a non-member would be 12 times x, which can be written as 12x.
For Seth to become a member, the cost would be a fixed $154, and then he would need to pay $5 each time he rents the court. So, the total cost of being a member would be 154 + 5x.
To find the point at which it becomes cheaper to be a member, we need to set up an inequality. We want the total cost of being a member (154 + 5x) to be less than the total cost of renting the court as a non-member (12x).
So, the correct inequality would be:
154 + 5x < 12x
To solve this inequality, we can start by subtracting 5x from both sides to isolate the x term:
154 < 12x - 5x
154 < 7x
Next, divide both sides by 7 to solve for x:
154/7 < x
22 < x
So, the correct conclusion is that Seth would need to rent the court more than 22 times for the membership to be cheaper than being a non-member. Hence, Seth is not correct in his initial assumption.