SOLUTION: 1. 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 membe
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Question 150991: 1. 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 mducky2(62) (Show Source): You can put this solution on YOUR website!
------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.
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