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 95401: 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?
*note* I really would like some help as to how to setup this question. Thank you!
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 original # of students be "x".
Original cost per student = 500/x dollars
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New # of students is "x-5"
New cost per student = 500/(x-5) dollars
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EQUATION:
new cost per student - old cost per student = 5 dollars
500/x - 500/(x-5) = 5
100/x - 100/(x-5) = 1
Multiply thru by x(x-5) to get:
100(x-5) - 100x = x(x-5)
-500 = x(x-5)
x^2-5x+500 = 0
(x-25)(x+20)=0
Positive solution:
x= 25 students (original # of students)
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Cheers,
Stan H.