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Questions
Seth is deciding whether or not he should become a member of the YMCA to use their volleyball courtsThe membership cost is $138 Members pay $7 to rent the volleyball courtsNon-members can rent the court also, but they have to pay $9 each timehow 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 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. To determine if becoming a member is cheaper than being a non-member in terms of court rental fees, we need to compare the total cost for both options.
For members, the cost is $138 for the membership fee plus $7 for each court rental. So, the total cost for members is given by the expression: 138 + 7x, where x is the number of times Seth rents the court.
For non-members, the cost is $9 for each court rental. So, the total cost for non-members is given by the expression: 9x, where x is the number of times Seth rents the court.
To find the number of times Seth would need to rent the court for the membership to be cheaper than being a non-member, we set up the inequality: 138 + 7x < 9x.
Now, let's solve the inequality to find the value of x:
138 + 7x < 9x
Subtract 7x from both sides:
138 < 2x
Divide both sides by 2:
69 < x
Since x represents the number of times Seth rents the court, we can conclude that Seth would need to rent the court at most 69 times for the membership to be cheaper than a non-membership.
Seth is incorrect in his setup of the inequality. Let's set up the correct inequality and solve it to determine the number of times Seth would need to rent the court.
Let's assume Seth rents the court x times.
For members, the cost of renting the court x times would be 7x.
For non-members, the cost of renting the court x times would be 9x.
According to the information given, Seth wants to find the number of times he needs to rent the court for the membership to be cheaper than a non-membership.
Therefore, the correct inequality would be:
138 + 7x < 9x
To solve this inequality, we first subtract 7x from both sides of the inequality:
138 < 2x
Next, we divide both sides of the inequality by 2:
69 < x
Simplifying further, we can rewrite this as:
x > 69
So the correct solution is that Seth would need to rent the court more than 69 times for the membership to be cheaper than a non-membership.
Seth's approach to setting up the inequality was correct, but his solution is incorrect. Let's go through the correct process step by step.
To determine how many times Seth needs to rent the court for the membership to be cheaper than being a non-member, we need to compare the costs.
For members, the cost is $138 for the membership plus $7 for each court rental. Therefore, the cost for members is given by the expression 138 + 7x, where x is the number of times Seth rents the court.
For non-members, the cost is simply $9 per court rental, regardless of the number of times it is rented.
Now, we can set up the inequality to compare the costs:
138 + 7x < 9x
To solve this inequality, we need to isolate x on one side of the equation. Let's subtract 7x from both sides:
138 < 9x - 7x
138 < 2x
Now, we can divide both sides by 2 to isolate x:
69 < x
So, the correct inequality is 69 < x.
This means that Seth would need to rent the court more than 69 times for the membership to be cheaper than being a non-member.
Therefore, Seth's incorrect answer makes it seem like becoming a member is cheaper, but the correct answer shows that Seth would need to rent the court more than 69 times for the membership to be the cheaper option.