Seth is deciding whether or not he should become a member of the YMCA to use their volleyball
courts. The membership cost is $154. Members pay $5 to rent the volleyball courts. Non-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 12x
154 27 X
22 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 correct in his inequality set up. The inequality is:
154 + 5x < 12x
To solve this inequality, we can subtract 5x from both sides:
154 < 7x
Next, we divide both sides by 7:
22 < x
So, Seth would need to rent the court at most 22 times for the membership to be cheaper than a non-membership.
Seth is deciding whether or not he should become a member of the YMCA to use their volleyball
courts. The membership cost is $154. Members pay $5 to rent the volleyball courts. Non-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 ≥ 12x
154 ≥7 X
22 ≥ 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's explanation and inequality are not correct. The correct inequality to compare the costs of being a member and a non-member is:
154 + 5x < 12x
To solve this inequality, we can subtract 5x from both sides:
154 < 7x
Next, we divide both sides by 7:
22 < x
This means that the number of times Seth would need to rent the court for the membership to be cheaper is more than 22 times, not at most 22 times.
Seth's initial inequality is partly correct, but there are some errors in the representation. Let's break down the information given:
1. The cost of membership is $154.
2. Members pay $5 each time to rent the volleyball courts.
3. Non-members pay $12 each time to rent the volleyball courts.
To determine the number of times Seth would need to rent the court for the membership to be cheaper than being a non-member, we need to compare the costs.
Let's denote "x" as the number of times Seth rents the court.
For non-members, the cost would be 12x (12 dollars per rental) since they pay $12 each time.
For members, the cost would be 154 + 5x (154 dollars for membership plus $5 per rental) since they have both the membership fee and the rental fee.
Now we can set up the correct inequality to solve the problem:
154 + 5x < 12x
To solve this, we need to isolate the "x" term:
154 < 12x - 5x
154 < 7x
Next, divide both sides of the inequality by 7:
154/7 < x
22 < x
So the correct answer is x > 22. This means Seth would need to rent the court more than 22 times for the membership to be cheaper than being a non-member.