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 132828: 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 checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
500/X=500/(X-5)-5
500/X-500/(X-5)=-5
(500(X-5)+X)/X(X-5)=-5
(500X-2500-500X)/(X^2+5X)=-5 CROSS MULTIPLY.
-5(X^2+5X)=-2500
-5X^2+25X+2500=0
-5(X^2-5X-500=0
-5(X-25)(X+20)=0
X-25=0
X=25 NUMBER OF STUDENTS ORIGINALLY PLANNED TO ATTEND.
PROOF:
500/25=500/(25-5)-5
20=(500/20)-5
25=25-5
20=20