SOLUTION: Some students planned 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 inc

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Question 58636This question is from textbook
: Some students planned 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?
I did my equation like this: x = he number of students
(x-5) + 5 = 500
x=500
Am I even close? This question is from textbook

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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?
Let original number of students be "x".
At $500 for the food each student would have paid 500/x dollars.
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When 5 did not show up there were "x-5" students
The average cost would now be 500/(x-5) dollars.
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EQUATION:
new average = old average +5
500/(x-5) = 500/x +5
100/(x-5) = 100/x + 1
100x = 100(x-5)+x(x-5)
100x = 100x-500+x^2-5x
x^2-5x-500=0
x=[5+-sqrt(25-4*-500)]/2
x=[5+-45]/2
x=25 or x=-20
Only the positive solution applies.
x=25 (original number of students)
Cheers,
Stan H.