Question 286423
Hello, 
We'll set up "x" as the number of members and "y" as the cost. From this we can set up 2 equations like this:
y=200,000/x
y-2000= 200,000/(x+5)
Make sense so Far?
OK, now plug the first equation into the second like this:
200,000/(x)-2000=200,000/(x+5) 
Get rid of the fractions by multiplying by (x)(x+5)to get:
200,000(x+5)-2000(x)(x+5)=200,000x Expand this out to be:
200,000x + 1,000,000 - 2000x^2 - 10,000x = 200,000x
Subtract 200,000x from both sides to get:
-2000x^2 - 10,000x + 1,000,000 = 0
Take out -2000 to be:
-2000(x^2+5x-500)=0 Factor this to get:
-2000(x-20)(x+25)=0
Now we know that :
x=-25 
x=20 
20 is the only reasonable answer so the number of members is:
20 members. 
You can check this out by dividing $200,000 by 20 members which is $10000 each has to pay. Adding 5 more members: divide $200,000 by 25 and we get $8000 each member pays. So it works out.  
Got it?
Good problem. 
RJ 
Check out a book I wrote:
www.math-unlock.com