At a local fitness center, members pay an $8 membership fee and $3 for each aerobics class . nonmembers pay $4 for each aerobics class. for what number of aerobics classes will the cost for members & nonmembers be the same?

This problem is an example of solving equations with variables on both sides. To solve, we must first set up an equation for both members and nonmembers. 

Since members pay $3 for each aerobics class, we can represent this part of the equation as 3c. Members also pay a one time $8 membership fee, so we just add the 8 to the 3c: 

3c + 8

Since nonmembers pay $4 for each aerobics class, we can represent this part of the equation as 4c. They do not have to pay a one time membership fee, so our equation will just be: 

4c

To determine when the cost (c) of the aerobics class will be the same for both members and nonmembers, we set the two equations equal to each other: 

3c + 8 = 4c

Then, we solve for c. First, the variables must be on the same side of the equation. We can do this by subtracting 3c from both sides of the equation: 

8 = 1c. 

Last, we divide both sides by 1. So c = 8. 

This means that the cost of classes will be the same for members and nonmembers at 8 classes. If we want to check our answer, we can plug 8 back into each equation: 

3c + 8 
= 3 ( 8 ) + 8
= 24 + 8
= 32

4c
= 4 ( 8 )
= 32