SOLUTION: A college charters a bus for $1900 to take a group of students to see a Broadway production. When 2 more students join the trip, the cost per student decreases by $2.50. How many s

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Question 992363: A college charters a bus for $1900 to take a group of students to see a Broadway production. When 2 more students join the trip, the cost per student decreases by $2.50. 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+ = the original number of students
+1900%2Fx+-+2.5+=+1900%2F%28+x+%2B+2+%29+
Multiply both sides by +x%2A%28+x%2B2+%29+
+1900%2A%28+x%2B2+%29+-+2.5%2Ax%2A%28+x%2B2+%29+=+1900x+
+1900x+%2B+3800+-+2.5x%5E2+-+5x+=+1900x+
+2.5x%5E2+%2B+5x+-+3800+=+0+
+25x%5E2+%2B+50x+-+38000+=+0+
+x%5E2+%2B+2x+=+1520+
Complete the square
+x%5E2+%2B+2x+%2B+%282%2F2%29%5E2+=+1520+%2B+%282%2F2%29%5E2+
+x%5E2+%2B+2x+%2B+1+=+1521+
+%28+x+%2B+1+%29%5E2+=+39%5E2+
+x+%2B+1++=+39+
+x+=+38+
38 students were in the original group
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check:
+1900%2Fx+-+2.5+=+1900%2F%28+x+%2B+2+%29+
+1900%2F38+-+2.5+=+1900%2F%28+38+%2B+2+%29+
+50+-+2.5+=+1900%2F40+
+47.5+=+47.5+
OK