<PRE><B>Question 314183</B>
A group of students agreed that each would chip in the same amount of money to pay for a party that cost $100.00.
 Then they found 5 more student interested in the party and in sharing the cost.
 This decreased the amount each had to pay by $1.00.
 How many students were involved in the party and how much did each student have to pay? 
:
Let x = no. of students finally involved
then
(x-5) = no. of students before 5 more joined
:
{{{100/x}}} = amt each had to pay
:
Before = after + $1
{{{100/(x-5)}}} = {{{100/x}}} + 1
multiply equation by x(x-5), results
100x = 100(x-5) + x(x-5)
:
100x = 100x - 500 + x^2 - 5x
combine on the right
0 = 100x - 100x + x^2 - 5x - 500
a quadratic equation
x^2 - 5x - 500 = 0
Factors to:
(x - 25)(x + 20) = 0
positive solution
x = 25 students finally involved
;
Find the cost: {{{100/25}}} = $4.00 per student
:
Check solution find the cost before
100/20 = $5, one dollar more</PRE>