SOLUTION: a fraternity charters a bus for a 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

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Question 442394: a fraternity charters a bus for a 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
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = number of students in original group
The cost per person of the original group was +360%2Fx+
+360%2Fx+-+2+=+360+%2F+%28+x+%2B+6+%29+
Multiply both sides by +x%2A%28+x%2B6+%29+
+360%2A%28x+%2B+6%29+-+2%2Ax%2A%28x%2B6%29+=+360x+
+360x+%2B+2160-+2x%5E2+-+12x+=+360x+
+2x%5E2+%2B+12x+-+2160+=+0+
+x%5E2+%2B+6x+-+1080+=+0+
Use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+6+
+c+=+-1080+
x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A%28-1080%29+%29%29%2F%282%2A1%29+
x+=+%28-6+%2B-+sqrt%28+4356+%29%29%2F2+
x+=+%28-6+%2B-+66%29%2F2+
x+=+%28-6+%2B+66%29%2F2+ (disregard negative square root)
+x+=+30+
There were 30 students in the original group
check:
+360%2Fx+-+2+=+360+%2F+%28+x+%2B+6+%29+
+360%2F30+-+2+=+360+%2F+%28+30+%2B+6+%29+
+12+-+2+=+360%2F36+
+10+=+10+
OK