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 84582: 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 venugopalramana(3286) About Me  (Show Source):
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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?
LET N BE NUMBER OF STUDENTS ATTENDED.
TOTAL NUMBER OF STUDENTS = N+5
FOOD BUDGET = 500 $
BUDGETED COST PER HEAD = 500/(N+5)
ACTUAL COST INCURRED PER HEAD ATTENDED = [500/(N+5)]+5 = (500+5N+25)/(N+5)
TOTAL ACTUAL COST =N*(5N+525)/(N+5)
HENCE
(5N^2+525N)/(N+5)=500
5N^2+525N=500(N+5)=500N+2500
5N^2+25N-2500=0
N^2+5N-500=0
N^2+25N-20N-500=0
N(N+25)-20(N+25)=0
(N-20)(N+25)=0
N=20
HENCE 20 ATTENDED THE FUNCTION