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? 
:
Let x = no. of students that attended
then
(x+5) = no. of planned students
:
Planned cost per student = {{{500/((x+5))}}}
Actual cost per student = {{{500/x}}}
:
Actual cost = planned cost + $5
{{{500/x}}} = {{{500/((x+5))}}} + 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