Seth is deciding whether or not he should become a member of the YMCA to use their volleyball court. The membership cost is $138. Members pay $7 to rent the volleyball courts. Non-membership 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 to be cheaper to be a member than a non-member?
Seth set up the following inequality to answer this question.
138 + 7 x greater than or equal to 9x
138 greater than or equal to 2x
69 greater than or equal to x
x less than or equal to 69
Seth would need to rent the court at most 69 times for the membership to be cheaper than a non-membership
Explain if the above inequality Seth set up is correct. If he is NOT correct, explain why by setting up the correct inequality and solve it.
Show all your work
Seth's inequality is correct.
The $138 membership cost plus the $7 rental fee per game must be less than or equal to the cost of renting the court as a non-member, which is $9 per game.
So, the inequality would be: 138 + 7x ≤ 9x
To solve this inequality, we can subtract 7x from both sides to get: 138 ≤ 2x
Then, divide both sides by 2 to isolate x: 69 ≤ x
This means that Seth would need to rent the court at most 69 times for the membership to be cheaper than renting as a non-member.
The inequality that Seth set up, 138 + 7x ≥ 9x, is not correct. To understand why, let's break down the problem and determine the correct inequality.
Let's denote the number of times Seth would need to rent the court as "x". As a member, Seth would pay a membership cost of $138 and $7 each time he rents the court. So, the total cost for Seth as a member would be 138 + 7x.
As a non-member, Seth would have to pay $9 each time he rents the court. Therefore, the total cost for Seth as a non-member would be 9x.
To determine when it becomes cheaper to be a member, we need to find the point at which the membership cost becomes less than the non-membership cost. Mathematically, this can be represented as:
138 + 7x < 9x
To solve this inequality, we can subtract 7x from both sides of the equation:
138 < 2x
Now, divide both sides by 2:
69 < x
So, the correct inequality is 69 < x, which means that Seth would need to rent the court more than 69 times for the membership to be cheaper than being a non-member.
In conclusion, Seth's initial inequality was incorrect. The correct inequality is 69 < x, which means Seth would need to rent the court more than 69 times for the membership to be cheaper than being a non-member.
The inequality that Seth set up is correct. Let's make sure by analyzing it step by step.
Given:
Membership cost = $138
Cost to rent the court for members = $7 per rental
Cost to rent the court for non-members = $9 per rental
To determine if it is cheaper for Seth to become a member rather than a non-member, we need to compare the total cost for both options. If the total cost for non-membership (renting the court individually) is greater than or equal to the membership cost, then it would be cheaper for Seth to become a member.
Let's use the inequality set up by Seth and evaluate it:
138 + 7x ≥ 9x
To solve this inequality, we can start by subtracting 7x from both sides of the inequality:
138 ≥ 2x
Next, divide both sides of the inequality by 2 to solve for x:
69 ≥ x
This tells us that x (the number of times Seth needs to rent the court) should be less than or equal to 69.
So, Seth would need to rent the court at most 69 times for the membership to be cheaper than being a non-member.
You show Seth's inequality as being 138 + 7x less than or equal to when in Seth's original inequality he has
138 + 7x is greater than 9x
138 greater than or equal to 2x
69 greater than or equal to x
x less than or equal to 69
So with your answer are you saying he is incorrect?
Apologies for the confusion. You are correct, my previous response was incorrect.
Seth's original inequality is indeed correct: 138 + 7x ≥ 9x
To solve this inequality, we can start by subtracting 7x from both sides:
138 ≥ 2x
Next, divide both sides by 2 to solve for x:
69 ≥ x
So, Seth would need to rent the court at most 69 times for the membership to be cheaper than renting the court as a non-member.
Apologies for the confusion in my previous response. Thank you for catching the mistake.