Question #33082

Let `n` be the number of aerobics classes where members and nonmembers pay the same cost in dollars.

Let's split this up:
Members: $8 + $2 per class
Nonmembers: $4 per class

Since `n` is where the cost will be the same for members and nonmembers, let's set the equation up.

`8 + 2n = 4n`
`8 = 2n`
`4 = n`
`n = 4`

To check our work, let's put 4 back into the equation:
`8 + 2(4) = 4(4)` ?
`8 + 8 = 16` ?
`16 = 16` Yes!

So 4 aerobics classes are when the cost for members and nonmembers are the same.

The price a member pays can be put into this equation:
`P_m = 8 + 2c`, where c is the number of classes.

The equation just says that each member will have to pay $8, even if they don't take any classes, and they will pay $2 for each class.

A nonmember's expense can be put into this equation:
`P_n = 4c`, where, again, c is the number of classes.

A nonmember does not have an extra flat fee. He only has to pay if he takes a class, and then he has to pay $4 for each.

Since we want to know when these two equations will give us the same answer, we can set them equal to each other:
`8 + 2c = 4c`

Then all we have to do is solve it.
`8 + 2c - 2c = 4c -2c`
`8 = 2c`
`8/2 = (2c)/2`
`4 = c`
`c = 4`

`P_m` and `P_n` will be equal when `c = 4`, i.e., when the member and nonmember have taken four classes.