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 o

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Question 186469: 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 ravelers?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = number of student in original group
Let c = the original cost per person
given:
(1) n%2Ac+=+360
(2) %28n+%2B+6%29%28c+-+2%29+=+360
(2) n%2Ac+%2B+6c+-+2n++-+12+=+360
Substitute (1) in (2)
(2) 360+%2B+6c+-+2n+-+12+=+360
(2) 6c+=+2n+%2B+12
(2) c+=+n%2F3+%2B+2
Substitute this in (1)
(1) n%2A%28n%2F3+%2B+2%29+=+360
(1) n%5E2%2F3+%2B+2n+-+360+=+0
(1) n%5E2+%2B+6n+-+1080+=+0
Use quadratic formula
n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+6
c+=+-1080
n+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A%28-1080%29+%29%29%2F%282%2A1%29+
n+=+%28-6+%2B-+sqrt%28+36+%2B+4320+%29%29%2F2+
n+=+%28-6+%2B-+sqrt%28+4356+%29%29%2F2+
n+=+%28-6+%2B-+66%29%2F2
n+=+60%2F2
n+=+30
There were 30 students in the original group
check:
(1) n%2Ac+=+360
(1) 30%2Ac+=+360
(1) c+=+12
and
(2) %28n+%2B+6%29%28c+-+2%29+=+360
(2) %2830+%2B+6%29%2812+-+2%29+=+360
(2) 36%2A10+=+360
(2) 360+=+360
OK