SOLUTION: The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to 5 more people to join the club so that the cost per person will decrease by

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Question 160728: The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to 5 more people to join the club so that the cost per person will decrease by $2,000. How many members are currently in the club?
Found 2 solutions by Fombitz, ankor@dixie-net.com:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let N be the number of members in the club now.
The per-person price now is,
PPN=200000%2FN
The per-person price when 5 more join is,
PPF=200000%2F%28N%2B5%29
You also know that,
PPF=PPN-2000
Substitute for your expression with N,
PPF=PPN-2000
200000%2F%28N%2B5%29=200000%2FN-2000
200000N=200000%28N%2B5%29-2000N%28N%2B5%29
200N=200%28N%2B5%29-2N%28N%2B5%29
200N=200N%2B1000-2N%5E2-10N%29
2N%5E2%2B10N-1000=0%29
N%5E2%2B5N-500=0
%28N%2B25%29%28N-20%29=0%29
.
.
.
N%2B25=0
N=-25
A negative answer doesn't make sense in our case.
N-20=0
N=20
There are 20 members currently.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
(2008-10-06 21:30:37): The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to 5 more people to join the club so that the cost per person will decrease by $2,000. How many members are currently in the club?
:
We can deal with this in $1000's Plane cost $200, cost decrease is $2
:
Let x = no. members currently in the club
then
200%2Fx = cost per member now
and
200%2F%28%28x%2B5%29%29 = cost if 5 more members join
:
The equation:
200%2Fx - 2 = 200%2F%28%28x%2B5%29%29
:
Multiply equation by x(x+5), results
200(x+5) - 2(x(x+5) = 200x
200x + 1000 - (2x^2 + 10x) = 200x
:
200x + 1000 - 2x^2 - 10x - 200x = 0
:
-2x^2 - 10x + 1000 = 0
:
Simplify divide equation by -2
+x^2 + 5x - 500 = 0
Factor
)x-20)(x+25) = 0
Positive solution
x = 20 members currently
:
:
Check solution find the actual costs
200000/20 = $10000
200000/25 = $8000