SOLUTION: The members of a flying club plan to share equally the cost of a $200000. airplaine. The members want to find five more people to join the club so that the cost per person will de

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Question 251089: The members of a flying club plan to share equally the cost of a $200000. airplaine. 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 $200000 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's deal in thousands of dollars, to eliminate some tedious typing
The plane cost 200, the decrease is 2
:
Let x = number of members in the club now
:
200%2Fx = cost per member now
and
200%2F%28%28x%2B5%29%29 = cost when 5 more join the club
:
Current cost - Cost with 5 more = 2 thousand
200%2Fx - 200%2F%28%28x%2B5%29%29 = 2
Multiply equation by x(x+5), results
200(x+5) - 200x = 2x(x+5)
:
200x + 1000 - 200x = 2x^2 + 10x
:
Combine like terms to form 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
200/20 - 200/25 =
10 - 8 = 2