SOLUTION: The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decr

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Question 146063This question is from textbook
: The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently in the club? This question is from textbook

Found 2 solutions by nerdybill, ankor@dixie-net.com:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently in the club?
.
Let x = number of members currently in the club
.
Current cost per member:
200000/x
.
If you added 5 new members, then the cost per member is:
200000/(x+5)
.
your equation:
[200000/x] - [200000/(x+5)] = 2000
solving for x will yield your answer
.
[200000/x] - [200000/(x+5)] = 2000
200000(x+5) - 200000(x) = 2000(x+5)(x)
200000x + 1000000 - 200000x = (2000x + 10000)(x)
1000000 = 2000x^2 + 10000x
0 = 2000x^2 + 10000x - 1000000
0 = x^2 + 5x - 500
.
factoring:
(x+20)(x-25)
Since you can't have "negative" members, the solution must be: 20

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently in the club?
:
Do this in thousands of dollars to avoid all those zero's
:
Let x = no. of members currently in the club
:
Cost per member
:
Original cost = Cost with 5 more + 2
= + 2
Multiply equation x(x+5) to get rid of the denominators
200(x+5) = 200x + 2x(x+5)
:
200x + 1000 = 200x + 2x^2 + 10x
:
Arrange on the left as a quadratic equation:
2x^2 + 10x + 200x - 200x - 1000 = 0
:
2x^2 + 10x - 1000 = 0
:
Simplify
x^2 + 5x - 500 = 0
:
Factor to:
(x+25)(x-20) = 0
:
Positive solution:
x = 20 original members
:
Check solution
Cost originally: 200/20 = 10k
Cost with 5 more: 200/25 = 8k