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?
Let x be the number of times Seth would need to rent the court for it to be cheaper to be a member than a non-member.
For members, the total cost would be 138 + 7x.
For non-members, the total cost would be 9x.
We can set up the inequality 138 + 7x < 9x and solve for x:
138 < 2x
69 < x
So Seth would need to rent the court at least 70 times for it to be cheaper to be a member than a non-member.
To find out how many times Seth would need to rent the court for it to be cheaper to be a member than a non-member, we can set up the following equation:
$138 + $7x < $9x
Where x represents the number of times Seth rents the court.
Let's solve the equation step-by-step:
1. Subtract $7x from both sides of the equation to isolate the variables on one side:
$138 < $9x - $7x
2. Simplify the right side:
$138 < $2x
3. Divide both sides of the equation by $2 to solve for x:
$138 / $2 < x
4. Simplify:
$69 < x
Therefore, Seth would need to rent the court more than 69 times for it to be cheaper to be a member than a non-member.
To determine how many times Seth would need to rent the court in order for it to be cheaper for him to become a member than a non-member, we need to compare the costs of being a member versus the costs of being a non-member.
Let's break it down:
- Membership cost: $138
- Cost per court rental for members: $7
- Cost per court rental for non-members: $9
First, let's calculate how many court rentals Seth would need as a member to make the membership cost worthwhile:
Membership cost ÷ Cost per court rental for members = $138 ÷ $7 = 19.71
Since you cannot have part of a rental, we will round the value up to the nearest whole number, making it 20 rentals.
Now, let's calculate the cost of 20 court rentals for non-members:
Cost per court rental for non-members × Number of rentals = $9 × 20 = $180
From the calculations, we can see that if Seth rents the court at least 20 times, it would be cheaper for him to become a member rather than paying as a non-member.
So, Seth would need to rent the court at least 20 times for it to be cheaper to become a member than a non-member.