SOLUTION: Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member i

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Question 124484: Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together
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Let the number of students be "x".
Average cost was 500/x dollars.
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Five did not show so there were "x-5" students
Average cost was 500/(x-5)
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EQUATION:
Original cost per student - New cost per student = 5 dollars
500/x - 500/(x-5) = 5
100/x - 100/x-5 = 1
-500 = x(x-5)
x^2-5x+500=0
(x-25)(x+20) = 0
Positive answer:
x=25 (original number of students)
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Cheers,
Stan H.