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
