Members at a yoga school pay $8 per class plus a one-time $90 membership fee. Non-members pay $12 per class. How many classes would a member have to take to save money compared to taking classes as a non-member?
N=number of classes at break-even
90+8N=12N
Solve for N and round the number to the next integer.
The solution to this problem is 23.
To find out how many classes a member would have to take to save money compared to taking classes as a non-member, we can set up an equation.
Let x be the number of classes a member would have to take.
For members, the cost per class is $8, and there is a one-time $90 membership fee. So the total cost for members is given by:
Cost for members = ($8 * x) + $90
For non-members, the cost per class is $12. So the total cost for non-members is given by:
Cost for non-members = $12 * x
To determine when a member will save money compared to a non-member, we need to equate the two costs and solve for x:
($8 * x) + $90 = $12 * x
Let's solve this equation step-by-step:
1. Distribute $8 to x:
$8x + $90 = $12x
2. Combine like terms by subtracting $8x from both sides:
$90 = $12x - $8x
3. Simplify the right side of the equation:
$90 = $4x
4. Divide both sides of the equation by $4:
($90 / $4) = (x)
The result is:
22.5 = x
However, since we can't have a fraction of a yoga class, we need to round up to the closest whole number of classes. Therefore, a member would need to take at least 23 classes in order to save money compared to taking classes as a non-member.
To determine how many classes a member would have to take to save money compared to a non-member, we need to compare the total cost for each scenario.
For a member:
- Cost per class: $8
- Membership fee: $90
For a non-member:
- Cost per class: $12
Let's assume that a member would have to take "x" number of classes to start saving money compared to a non-member.
For a member, the total cost would be the sum of the membership fee and the cost per class multiplied by the number of classes:
Total cost for a member = Membership fee + (Cost per class * Number of classes)
For a non-member, the total cost would be the cost per class multiplied by the number of classes:
Total cost for a non-member = Cost per class * Number of classes
Since we want to find the point where a member saves money compared to a non-member, we can set up an equation:
Membership fee + (Cost per class * Number of classes) < Cost per class * Number of classes
Simplifying the equation:
Membership fee < Cost per class * Number of classes - Cost per class * Number of classes
Membership fee < 0
However, we cannot have a negative membership fee, so it means that a member would never save money compared to a non-member.