There is an initiation fee to join the Pine River Country Club, as well as monthly dues.

Question

The total cost after 7 months' membership will be $3,175, and after 1.5 years, $4,110. Find both the initiation fee and the monthly dues.

Answer 1

Write down the information you need:

7 months + initiation fee = $3,175

 

Change 1.5 years to 18 months...

18 months + initiation fee = $4,110

 

Subtract the two membership totals:

$4,110-$3,175 = $935

This tells you that months 8 through 18 (11 month span) cost $935. 

 

Divide $935 by 11 months:

This tells you each month costs $85 for the monthly dues. 

 

Find the initiation fee:

7 months *$85 = $595, but including the initiation fee the total is $3,175.

Find the difference: $3,175-$595 = $2,580. 

 

Check the initiation fee with the other membership span of 1.5 years:

18 months * $85 = $1,530, but including the initiation fee the total is $4,110. 

Find the difference: $4,110-$1,530 = $2,580. 

The difference is the initiation fee. 

Answer 2

I: Initiation fee

C: Monthly dues

 

I+7C=3175 ( total cost after 7 months is initiation fee + 7 monthly payments)

I+18C=4110 (total cost after 1.5 years (18 months) is initiation fee + 18 monthly payments)

 

Solve both equations for C

subtract the second equation from the first

18C-7C=4110=3175 ------>C=85

 

substituting in one of the above equations

I+7(85)=3175 ------->I=2580

 

Therefore the initiation fee is $2580 and the monthly due is $85