At a local fitness​ center, members pay an ​$8 membership fee and ​$3 for each aerobics class. Nonmember

Question

At a local fitness center, members pay an

$8

membership fee and $3

for each aerobics class. Nonmembers pay $5

for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?

 

Answer 1

What is the unknown quantity in this problem, Kevin? It is the total number of classes that will produce the same cost for members and nonmembers. We will represent that by the variable x. The cost for members can then be expressed as the membership fee + (the cost per class x the total number of classes). The membership fee is 8.00, and each class is 3.00. Algebraically, this is written as:

 

8 + 3x = cost for members

 

The cost for nonmembers is simply the cost per class times the total number of classes. This is the algebraic expression 5x.

 

Our task is to determine when does the cost for members equal the cost for nonmembers. So we set the two above expressions equal to each other and solve for x.

 

8 + 3x = 5x

 

Can you solve this equation for x, Kevin?