SOLUTION: 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
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Question 314183: 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? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! 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
: = amt each had to pay
:
Before = after + $1 = + 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: = $4.00 per student
:
Check solution find the cost before
100/20 = $5, one dollar more
