algebra repost
posted by Melissa on .
Sharing cost. The members of a 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 = the number of members currently in the club
200,000/x = 200,000/(x+5) + 2000
Multiply to eliminate fractions.
200,000(x+5) = 200,000x + 2000(x)(x+5)
200,000x + 1,000,000 = 200,000x + 2000x^2 + 10,000x
1,000,000 = 2000x^2 + 10,000x
2000x^2 + 10,000x  1,000,000 = 0
Divide by 2000.
x^2 + 5x  500 = 0
(x+25)(x20) = 0
x = 20, 25
The answer of x=25 does not make sense in the context, so we are left with x=20 people. 
Sharing cost. The members of a 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?