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

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Question 94570: 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 ankor@dixie-net.com(22740) 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 x = Number of students, who actually attended
Then
(x+5) = Original number of students expected
:
Actual cost per person: = 500%2Fx
:
Expected cost per person = 500%2F%28%28x%2B5%29%29
:
It said the cost increased by $5, because of of 5 less students:
Actual cost - expected cost = $5
500%2Fx - 500%2F%28%28x%2B5%29%29 = 5
:
multiply equation by x(x+5) to get rid of the denominators, resulting in:
500(x+5) - 500x = 5(x(x+5)
:
500x + 2500 - 500x = 5x^2 + 25x
:
Arrange as a quadratic equation:
5x^2 + 25x - 2500 = 0
:
Simplify divide by 5:
x^2 + 5x - 500 = 0
:
Factors to:
(x+25)(x-20) = 0
:
x = +20, the positive solution is what we want here.
:
20 Students actually attended
:
:
Check our solution. Actual = 20, Expected no. of student = 25
500/20 - 500/25 =
25 - 20 = $5