Question 125815
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 students anticipated to attend
:
The original cost per student for food: {{{500/((x+5))}}}
Actual cost per student: {{{500/x}}}
:
The equation
Actual cost - original cost = $5
{{{500/x}}} - {{{500/((x+5))}}} = 5
:
Multiply each term by x(x+5) to get rid of the denominators. cancel them & you have:
500(x+5) - 500x = 5*x(x+5)
:
500x + 2500 - 500x = 5x^2 + 25x
:
5x^2 + 25x - 2500 = 0; 500x's cancel, arrange as a quadratic equation
:
Simplify divide eq by 5:
x^2 + 5x - 500 = 0
:
Factors to:
(x + 25) (x - 20) = 0
:
Positive solution is what we want:
x = +20 students actually attended
;
:
Check solution by finding the cost per student
original 500/25 = 20
actual:  500/20 = 25
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difference cost =  5