Question 150991
------If x represents the original amount of students attending
cost of food before = 500/x
cost of food after = 500/(x-5)
price increase = 5

------Since the cost of food after is $5 more than the cost of food before:

(500/x)+ 5 = [500/(x-5)]
[(500/x)+5] * x(x-5) = [500/(x-5)] * x(x-5)
500(x-5) + 5x(x-5) = 500x
500x - 2500 + 5x^2 - 25x = 500x
500x - 500x - 2500 + 5x^2 - 25x = 500x - 500x
5x^2 - 25x - 2500 = 0
x^2 - 5x - 500 = 0
(x+20)(x-25) = 0
x + 20 = 0    OR    x - 25 = 0
x = -20  OR  x = 25
-------It only makes sense if there are a positive number of students. Therefore, there must have been 25 original students. After 5 left, that would be mean there are 25 - 5 students, or 20 students remaining.