SOLUTION: please help me solve this word problem The members of the flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join

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Question 185177: please help me solve this word problem
The members of the 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 the 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. currently in the club
:
Let's do the problem in thousands of dollars to avoid writing all those 0's
:
200%2Fx = cost per person currently
then
200%2F%28%28x%2B5%29%29 = cost per person when 5 are added
:
Present cost/member - $2k = Cost/member when 5 are added:
200%2Fx - 2 = 200%2F%28%28x%2B5%29%29
Multiply equation 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 and you have:
200(x+5) - 2x^2 - 10x = 200x
:
200x + 1000 -(2x^2 + 10x) = 200x
:
200x + 1000 - 2x^2 - 10x - 200x = 0
Combine like terms
-2x^2 - 10x + 1000 = 0
Simplify and change the signs, divide by -2
+x^2 + 5x - 500 = 0
factor
(x+25)(x-20) = 0
positive solution:
x = 20 members currently
:
:
Check solution; find the cost per member
currently: 200k/20 = 10k
plus five: 200k/25 = 8k