You are to choose between two health clubs. Club A offers membership for a fee of $11 plus a monthly fee of $14. Club B offers membership for a fee of $29

Question

Plus a monthly fee of $5. After how many months will the total cost of each health club be the same? What will be the cost for each club? 

Answer 1

Hi Elliot,

 

The easiest way to solve this is to take the unknown variable (number of months) and call that x.

 

We want to know when the cost of gym A will equal gym B. SO...

 

The cost of gym A is: 11 + 14x

The cost of gym B is :29 + 5x

 

If we set these expressions equal to each other and solve for x:

11+14x=29+5x

9x=18

X=2

Therefore, in two months the cost will be the same. If we plug in 2 in either expression...

11 +14(2)

11+28

39!

 

Each gym will cost $39 for two months of membership.

 

Hope this helps you learn how to set these up!

Answer 2

Let 'm' be the number of months.  Then:

Club A: 11+14m

Club B: 29+5m

 

Now set these two expressions equal to each other:

11+14m=29+5m

--> 9m=18

--> m=2

--> after two months, you will have spent the same amount at each club.

 

Lastly, evaluate either of the original expressions (doesn't matter which) to come up with the amount spent after two months.  I am going to use the expression for Club A:

11+14(2) = 11 + 28 = $39.00.