SOLUTION: This is an online study course. 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

Question 106572This question is from textbook
: This is an online study course.
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?
500/x + 5 = 500/(x-5)
This question is from textbook

Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
500/x + 5 = 500/(x-5)
-----------------------------
500/x is the original "cost per person" for the group
-------------
500/(x-5) is the new "cost perperson" for the group after 5 fail to show.
----------------
EQUATION:
(500/x) + 5 + 500/(x-5)
Multiply thru by x(x-5) to get:
500(x-5) + 5x(x-5) = 500x
500x - 2500 = 5x^2-25x = 500x
5x^2-25x-2500 = 0
x^2 - 5x - 500 = 0
x = [5 +- sqrt(25-4*-500)]/2
x = [5 +- sqrt(2025]/2
x = [5 +- 45]/2
x = 25 or x = -20
---------
x=20 is the only realistic answer.
x-5 = 15 (number who attended the get-together)
==============
Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
500/x + 5 = 500/(x-5)
:
I would do it this way:
Let x = actual number that attended:
Then
(x+5) = number that was anticipated to come
:
Anticipated cost + $5 = Actual cost
+ 5 =
:
Multiply equation by x(x+5)
500x + 5(x(x+5)) = 500(x+5)
500x + 5x^2 + 25x = 500x + 2500
:
Arrange as a quadratic on the left:
5x^2 + 500x - 500x + 25x - 2500 = 0
5x^2 + 25x - 2500 = 0
:
Simplify, divide by 5
x^2 + 5x - 500 = 0
:
Factors to:
(x+25)(x-20) = 0
:
x = +20 is the solution we want here
:
20 actually attended
:
Actual cost 500/20 = $25 each
:
If 25 attended:
500/25 = $20, $5 less
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