You are choosing between two health clubs Club A offers memb

You are choosing between two health clubs. Club A offers membership for a fee of $ 28$28 plus a monthly fee of $ 22.$22. Club B offers membership for a fee of $ 16$16 plus a monthly fee of $ 28.$28. After how many months will the total cost of each health club be the same? What will be the total cost for each club?

In___months the total cost of each health club will be the same.

The total cost for each health club will be $___ .

Solution

Club A offers membership fee $28 that is fix charges = $28.

And monthly charges $22 that is variable charges per month is = $22.

Let us assume the number of months be x.

So, we can set a function for total fee of Club A as f(x) = 22x + 28.

On the same way..

Club B offers membership fee $16 that is fix charges = $16.

And monthly charges $28 that is variable charges per month is = $28.

So, we can set another function for total fee of Club B as g(x) = 28x + 16.

When total cost of both Clubs would be equal the above two functions would also be equal.

Therefore,

f(x)= g(x)

22x + 28 = 28x+16

Subtracting both sides by 28.

22x +28-28 = 28x +16 - 28

22x = 28x -12.

Subtracting both side 28x.

22x-28x = 28x -12-28x.

-6x = -12

Dividing both sides by -6.

-6x/-6= -12/-6

x= 2.

So, for two months the cost of both clubs would be same.

Plugging x=2 in any of the function.

f(x)= 22x +28

f(2) = 22*2 +28 = 44+28

f(2) = $72.

So, after 2 months total cost would be $72.

In 2 months the total cost of each health club will be the same.

The total cost for each health club will be $72.