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

Question 424429: The members of the flying club plan to share equally the cost of a $200,000 airplane. Teh 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?
a. 20
b. 25
c. 10
d. 15
e. 30
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let x = the number of members currently in the club
The current cost per member = 200000/x
We want the NEW cost per member to be $2000 less than the current cost.
So the equation we need to solve is 200000/(x+5) = 200000/x - 2000
This says that the new cost (2000000/(x+5)) is equal to the original cost minus $2000.
Now solve for x: 200000/(x+5) = 2000(100/x - 1) -> 100/(x+5) = 100/x - 1
100/(x+5) = (100 - x)/x -> 100x = (x+5)(100-x) -> 100x = 100x - x^2 + 500 - 5x
x^2 + 5x - 500 = 0 -> x = (-5 +- sqrt(25 + 2000))/2
Take the positive solution: x = (-5 + 45)/2 = 20
So there are currently 20 members in the club
Check: 200000/25 = 200000/20 - 2000 -> 8000 = 10000 - 2000 = 8000
Ans: a
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