Solving a System with Substitution

Question

At a local fitness center, members pay a six dollar membership fee and $3 for each aerobic class. Nonmembers pay $4 dollars for each aerobic class. For what number of aerobic classes will cost nonmembers and members be the same?

Answer 1

Actually, you only need one equation to solve this problem.

 

let c=the number of  aerobic classes  for which a member Or a non-member pay the same total cost("c" is the only UNKNOWN in the problem)

 

From the problem we translate the following:

 

Total cost for members=$6(the fixed price)+3(cost/class for members)*c(number of classes)

Total cost for non-members=4(cost/class for nonmembers)*c(number of classes)

 

We want the total cost for members to be equal to the total cost for non-members. This translates into:

 

$6(the fixed price)+3(cost/class for members)*c=4(cost/class for nonmembers)*c, which, more simplified looks like this:

 

6+3*c=4*c. Subtract 3c on both sides

6=c, Or

c=6 classes.

 

Please let me know if you have any more questions.

Thanks

Adina

 

 

 

 

 

Answer 2

Let's say that m represents the amount of money members pay for aerobic classes at the fitness center. 

The cost of the aerobic classes for members is defined by this simple equation:  m = 6 + 3x

That is, members will pay a $6 fee to the fitness center, plus $3 every time they take aerobic classes.

Now, let's say that n represents the amount of money nonmembers pay for aerobic classes.

The cost of the aerobic classes for nonmembers is defined by this simple equation:  n = 4x

That is, nonmembers pay $4 for every aerobic class they take at the fitness center.

Alas! in both equations, x represents the number of classes taken. 

Now, if we want to know for what number of classes m and n will be equal; simply, let's set them equal:

If m = 6 + 3x,  n = 4x  and n = m, then 6 + 3x = 4x 

Solving for x, we find that, when n = m, x = 6

What did we say x was??  Oh, yes! the number of classes taken. Then, the cost for members and nonmembers will be equal when they take 6 classes.

A word of advise: If you're going to take less than 6 classes, do not bother buying the membership.  If you're an aerobics enthusiast, love the classes at that fitness center and expect to take more than six classes per month, then buy the membership.  Perhaps you will also enjoy working out at the thread mill, or the weight room.  Decisions, decisions...