SOLUTION: Sharing cost. 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

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Question 293931: Sharing cost. 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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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 = no. of members
then
(x+5) = no. of members to decrease the cost by 2k
:
We can do this in 1000's of dollars
:
Current cost per member = 200%2Fx
:
Cheaper cost per member = 200%2F%28%28x%2B5%29%29
:
Current cost = new cost plus two thousand
200%2Fx = 200%2F%28%28x%2B5%29%29 + 2
multiply by x(x+5), results
200(x+5) = 200x + 2x(x+5)
:
200x + 1000 = 200x + 2x^2 + 10x
can be arranged as a quadratic equation
2x^2 + 10x - 1000 = 0
simplify, divide by 2
x^2 + 5x - 500 = 0
Factor
(x + 25)(x - 20) = 0
positive solution
x = 20 members currently
:
:
Check solution by finding the costs
200000/20 = 10000
200000/25 = 8000
-----------------
difference: 2000