Question

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?

Answer 1

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