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 d

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Question 205411: 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):
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 = no. of members in the club
then
(x+5) = no. of members when 5 more join
:
Do the problem in 1000's of dollars to reduce typing 0's
:
Cost per member now: 200%2Fx
Cost per member later: 200%2F%28%28x%2B5%29%29
:
the equation:
200%2Fx - 2 = 200%2F%28%28x%2B5%29%29
Multiply by x(x+5)
x(x+5)*200%2Fx - 2x(x+5) = x(x+5)*200%2F%28%28x%2B5%29%29
cancel out the denominators
200(x+5) - 2x^2 - 10x = 200x
:
200x + 1000 - 2x^2 - 10x = 200x
Arrange as a quadratic eq on the right
0 = 2x^2 + 10x + 200x - 200x - 1000
:
2x^2 + 10x - 1000 = 0
Simplify, divide by 2
x^2 + 5x - 500 = 0
Factor to:
(x+25)(x-20) = 0
Positive solution:
x = 20 members now.
;
;
Check solution:
200/20 = 10
200/25 = 8
-------------
differ = 2 thousand dollars