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

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
RELATED QUESTIONS
A group of students agreed that each would chip in the same amount to pay for a party... (answered by solver91311)

a) On a 135-mile bicycle excursion, Maria averaged 5 miles per hour faster for the first... (answered by solver91311)

A group of friends planned to chip in to raise a total of $100 for a party but 5 people... (answered by josgarithmetic,ikleyn)

A group of co-workers agreed that each would contribute the same amount to buy their boss (answered by stanbon)

Students in a school agreed to buy a trophy that would be presented to the winning soccer (answered by richwmiller)

In a benefit show, a number of wealthy men agreed that the first one to arrive would pay... (answered by josgarithmetic)

I need help writing a function for the following problem: "Roy's hometown newspaper... (answered by cowess)

. Tom, Dick, and Mary decided to share expenses for a class party. Tom bought $28 worth... (answered by jojo14344)

Tom, Dick and Mary decided to share expenses for a class party. Tom bought $28 worth of... (answered by ankor@dixie-net.com,Mathtut)