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 144622: 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?

Found 2 solutions by ankor@dixie-net.com, shahid:
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 = no. of students that attended
then
(x+5) = no. of planned students
:
Planned cost per student = 500%2F%28%28x%2B5%29%29
Actual cost per student = 500%2Fx
:
Actual cost = planned cost + $5
500%2Fx = 500%2F%28%28x%2B5%29%29 + 5
Multiply equation by x(x+5), resulting in:
500(x+5) = 500x + 5x(x+5)
:
500x + 2500 = 500x + 5x^2 + 25x
:
Arrange as a quadratic equation:
5x^2 + 25x - 2500 = 0
Simplify
x^2 + 5x - 500 = 0
Factor:
(x+25)(x-20) = 0
positive solution
x = 20 students actually attended
:
:
Check solution by finding the cost of each
500/20 = 25
500/25 = 20

Answer by shahid(44) About Me  (Show Source):