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 their 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 to 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 is correct in his answer. He correctly set up the inequality 154 + 5x ≥ 12x, which represents the total cost of being a member (154 + 5x) being greater than or equal to the total cost of renting the court as a non-member (12x).
To solve this inequality, Seth subtracted 5x from both sides to get 154 ≥ 7x. Then he divided both sides by 7 to isolate x, which gave him 22 ≥ x. This means that Seth would need to rent the court at most 22 times for the membership to be cheaper than a non-membership.
So, Seth is correct in stating that if he rents the court at most 22 times, it would be cheaper for him to become a member of the YMCA.
Seth is correct in setting up the inequality, but he made an error in solving it.
The inequality he set up is:
154 + 5x ≥ 12x
To solve this inequality, we need to isolate the variable x on one side.
Let's correct Seth's error in solving the inequality:
154 + 5x ≥ 12x
We can subtract 5x from both sides of the inequality to get:
154 ≥ 12x - 5x
This simplifies to:
154 ≥ 7x
Now, we want to solve for x, so we can divide both sides of the inequality by 7:
154/7 ≥ x
This simplifies to:
22 ≥ x
So, Seth made a mistake in his final statement. The correct inequality should be x ≤ 22, which means that Seth would need to rent the court at most 22 times for the membership to be cheaper than a non-membership.
Seth is not correct. The inequality he set up, 154 + 5x ≥ 12x, is incorrect because it assumes that Seth will pay $5 per rental as a member and $12 per rental as a non-member. However, as a member, Seth will actually pay $5 per rental, regardless of how many times he rents the court.
To set up the correct inequality, we can assume that Seth will rent the court x times as a member. As a member, he will pay $5 per rental, so the total cost will be 5x. As a non-member, Seth will pay $12 per rental. Since Seth wants to know when it becomes cheaper to be a member than a non-member, we need to compare the cost of membership to the cost of renting as a non-member.
The correct inequality is:
154 + 5x < 12x
To solve this inequality:
154 < 7x (subtract 5x from both sides)
22 < x
So, the correct answer is x > 22. Seth would need to rent the court more than 22 times for the membership to be cheaper than renting as a non-member.