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 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 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 correct explain why by setting up the correct inequality and solve it
Seth is not correct in his inequality.
Let's assume Seth rents the court x times.
For a member, the cost of renting the court would be $5 per rental, so the total cost for x rentals would be 5x.
For a non-member, the cost of renting the court would be $12 per rental, so the total cost for x rentals would be 12x.
Seth wants to find out when it is cheaper to be a member than a non-member, so we can set up the following inequality:
5x ≤ 154 + 12x
By subtracting 12x from both sides, we get:
-7x ≤ 154
To isolate x, we divide both sides by -7, remembering to change the inequality sign since we're dividing by a negative number:
x ≥ -154/7
Since Seth cannot rent the court a negative number of times, we discard the negative solution.
Therefore, the correct inequality is:
x ≥ 22
This means Seth would need to rent the court at least 22 times for the membership to be cheaper than a non-membership.
Seth's setup of the inequality is incorrect. Let's break it down to see where the mistake lies:
He assumed that the cost for members to rent the volleyball courts is $5 per time, while non-members have to pay $12 per time. However, this assumption is incorrect. Both members and non-members have to pay the same rental fee of $5 per time.
To calculate the cost for Seth to be a member, we can set up the following inequality:
Membership Cost + (Number of times rented * Rental fee for members) ≤ Number of times rented * Rental fee for non-members
Using the given values, the inequality becomes:
154 + 5x ≤ 12x
Now let's solve this revised inequality:
Subtract 5x from both sides of the equation:
154 ≤ 12x - 5x
154 ≤ 7x
Divide both sides of the equation by 7:
154/7 ≤ x
Simplifying the left side:
22 ≤ x
This means that Seth would need to rent the court at least 22 times for the membership to be cheaper than being a non-member.
Therefore, Seth's statement is correct.
Seth's approach is incorrect. The correct way to set up the inequality is as follows:
Let x represent the number of times Seth would need to rent the court.
For non-members:
Cost of renting the court = $12 per time
Total cost for x times = 12x
For members:
Membership cost = $154 (paid once)
Cost of renting the court = $5 per time
Total cost for x times = 154 + 5x
To find when it is cheaper for Seth to be a member, we need to set up the inequality:
12x > 154 + 5x
Simplifying the inequality:
12x - 5x > 154
7x > 154
x > 154/7
To find the exact value, we divide 154 by 7:
154 ÷ 7 = 22
So Seth's original answer is correct. Seth would need to rent the court more than 22 times for the membership to be cheaper than being a non-member.