SOLUTION: A fraternity charters a bus for a ski trip at a cost of $360. When 6 more students join the trip, each person's cost decreases by $2. How many students were in the original group

Question 26423: A fraternity charters a bus for a ski trip at a cost of $360. When 6 more students join the trip, each person's cost decreases by $2. How many students were in the original group of travelers?
This is my work.
6(x-2)(x-2)=360
6x squared -24x + 24 -360=0
Found 2 solutions by Paul, stanbon:
Answer by Paul(988) (Show Source): You can put this solution on YOUR website!
Let the orignial group be x
(x+6)(360-2x)
360x+2160-2x^2-12x=0,x
-2x^2+348x+2160=0,2
2x^2-348x-2160
Factor:
x=-6 and x=180
Remove the negative.
Hence, there were 180 orginal goup of travellers.
Paul.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let original number of students be "x"
Their individual cost is 360/x
If six more join there are now "x+6"
Individual cost for this expanded group would be 360/(x+6)
But this last individual cost is $2 less than the original individual cost.
EQUATION:
Original indiv. cost - New indiv cost = $2
360/x - 360/(x+6)= 2
1/x -1/(x+6)= 1/180
6/[x(x+6)] = 1/180
x^2+6x-1080=0
(x+36)(x-30)=0
x=30 (size of original group)
Cheers,
stan H.
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