SOLUTION: Some students planned a get together. The budget for the 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 89907: Some students planned a get together. The budget for the 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(57361) About Me  (Show Source):
You can put this solution on YOUR website!
Some students planned a get together. The budget for the 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 number of students be "x".
Budget was $500 or average of $500/x per student
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Five no-shows leaves "x-5" students with average of $500/(x-5)
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EQUATION:
new average - old average = $5
500/(x-5) - (500/x) = 5
Multiply thru by x(x-5) to get:
500x - 500(x-5) = 5x(x-5)
500x - 500x+ 2500 = 5x^2-25x
5x^2-25x-2500 = 0
x^2-5x-500=0
x = [5+-sqrt(5^2-4*-500)]/2
Positive answer only:
x = [5+sqrt(2025)]/2
x = [5+45]/2
x = 25 students
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Cheers,
Stan H.