SOLUTION: A college charters a bus for $1300 to take a group to a museum. When fourteen more students join the trip, the cost per student drops by $17.50. How many students were in the origi

Question 347340: A college charters a bus for $1300 to take a group to a museum. When fourteen more students join the trip, the cost per student drops by $17.50. How many students were in the original group?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A college charters a bus for $1300 to take a group to a museum. When fourteen more students join the trip, the cost per student drops by $17.50. How many students were in the original group?
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Let the original # in the group be "x".
Cost per students was 1300/x dollars.
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The # in the revised group is (x+14).
Cost per student is 1300/(x+14) dollars.
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Equation:
old average - new average = 17.50
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1300/x - 1300/(x+14) = 17.50 dollars
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Multiply thru by x(x+14) to get:
1300(x+14) - 1300x = 17.5x(x+14)
1300*14 = 17.5x^2 + 245x
17.5x^2 + 245x - 18200 = 0
17.5(x^2 + 14x - 1040) = 0
(x+40)(x-26) = 0
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Positive solution:
x = 26 (# in the original group)
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Cheers,
Stan H.

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