SOLUTION: Hi, can you help me with this one? 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 theref

Question 205918: Hi, can you help me with this one?
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?
Thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
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Original number: x students
Average cost per student: 500/x dollars
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New number: x-5 students
Average cost per student: 500(x-5) dollars
-------------------------------
Equation:
new cost - old cost = 5 dollars
500/(x-5) - 500/x = 5
500x - 500x + 2500 = 5x(x-5)
2500 = 5x^2-25x
x^2-45-500 = 0
(x-25)(x+20) = 0
Positive solution:
x = 25 (original number in the group)
==========================================
Cheers,
Stan H.
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