Question
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 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
Answers
GPT 3.5
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.
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.