Find the number of months you must be a member to have the same cost for each cost.

Question

Two different golf country clubs have the following membership fees and monthly costs. Ludwig's Fast 18 charges $100 membership fee and then $30 a month. Ocean Shore Country Club charges a $160 membership fee and then $10 a month. Find the number of months you must be a member to have the same cost for each cost.

 

Answer 1

Each country club has a "fixed cost" and a "variable cost."  The fixed cost is charged even if you immediately cancel membership (that is, 0 months).  The variable cost is charged based on the number of months because --

        (cost per month)*(number of months)           gives variable cost; months cancel out

 

Let x = number of months

 

                LF18:                      OSCC

         $100 + ($30)x   =    $160 + ($10)x

               ($20)x  = $60                           [subtract $10x and subtract $100 from both sides]

                    x = 3 months                        [divide both sides by 20]

 

p.s., Show your smarts, this is called "the break even point"

Answer 2

Ludwig's Fast 18

$100 + 30m where m = # months of membership

 

Ocean Shore

$160 + 10m where m = # months of membership

 

We want to determine the number of months of membership where these two expressions will be equal.

100 + 30m = 160 + 10m

20m = 40

m = 2

 

So at 1 month, Ocean Shore will be more expensive

At 2 months, the two will be the same

At 3 months and more, Ludwig's will be the costlier option.