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.