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.