Seth is deciding whether or not he should become a member of the YMCA to use their volleyball courts. The membership cost is $138. Members pay $7 to rent the volleyball courts. Non-members can rent the court also, but they have to pay $9 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.
138 + 7x ≥ 9x
138 ≥ 2x
69 ≥ x
x ≤ 69
Seth would need to rent the court at most 69 times for the membership to be cheaper than the non-membership.
Explain if Seth is corrrect. if he is not correct, explain why by setting up the correct inequality and solve it
Seth is correct. The inequality 138 + 7x ≥ 9x represents the total cost of being a member ($138 plus $7 per rental) being greater than or equal to the total cost of being a non-member ($9 per rental). By subtracting 7x from both sides of the inequality, we get 138 ≥ 2x, which is equivalent to x ≤ 69. This means that for Seth, renting the court fewer than or equal to 69 times would make the membership cheaper than being a non-member.
Seth is correct in setting up the inequality as 138 + 7x ≥ 9x, but he made a mistake in solving it. Let's correct it:
The inequality is set up correctly as 138 + 7x ≥ 9x.
To solve it, we need to isolate the variable x. Start by subtracting 7x from both sides of the equation:
138 ≥ 2x.
Now, divide both sides of the equation by 2:
69 ≥ x.
Therefore, the corrected inequality is x ≤ 69.
Now we can interpret the inequality. It states that Seth would need to rent the court at most 69 times for the membership to be cheaper than the non-membership option. Thus, Seth is correct in his answer, and if he plans to rent the court 69 times or fewer, it would be more cost-effective for him to become a member.
Seth is partially correct in setting up the inequality, but he made a mistake in the last step. Let's analyze his setup first:
We can start by setting up the inequality as: 138 + 7x ≥ 9x, where x represents the number of times Seth rents the court.
This inequality represents the total cost if Seth chooses to become a member. The left side of the inequality, 138 + 7x, represents the membership cost of $138 plus $7 for each rental. The right side of the inequality, 9x, represents the cost if Seth chooses not to become a member and pays $9 for each rental.
Now let's solve Seth's inequality step by step:
138 + 7x ≥ 9x
Subtract 7x from both sides to isolate the x term:
138 ≥ 9x - 7x
138 ≥ 2x
Divide both sides by 2 to solve for x:
69 ≥ x
According to Seth's calculation, x should be less than or equal to 69 for the membership to be cheaper than being a non-member.
However, Seth made a mistake in the last step. If we analyze the inequality, we'll notice that if x is less than or equal to 69, both sides of the inequality hold true. But, if x exceeds 69, the inequality will no longer hold true.
To determine the correct inequality and find the accurate number of times Seth needs to rent the court, we need to consider the break-even point – the point where the membership cost becomes equal to the cost of being a non-member.
Let's set up the correct inequality and solve it:
138 + 7x ≥ 9x
Subtract 7x from both sides:
138 ≥ 2x
Divide both sides by 2:
69 ≥ x
So, the correct inequality is 69 ≥ x, which means Seth needs to rent the court at most 69 times for the membership to be cheaper than being a non-member. Therefore, Seth's answer is indeed correct.