<PRE><B>Question 106572</B>
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
{{{500/((x+5))}}} + 5 = {{{500/x}}}
:
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</PRE>