algebra word problem

Question

A group of students agreed that each would chip in the same amount to pay for a party that would cost $100. Then they found 5 more students interested in the party and in sharing the expenses. This decreased the amount each had to pay by $1. How many students were involved in the party and how much did each student have to pay?

Answer 1

Set up two equations. Then solve for one variable to plug in and check it satisfies what we're looking for. (I used the quadratic formula)

X = original # of students

Y= amount x is divided by to know amount each student pays

Set up 2 equations

x/y (y) = 100

(x + 5 ) / y = y - 1 (1 dollar less per student after 5 more chip in)

Based on first equation, x = 100

Plug in for second equation and end up with y² - y - 105 = 0

Plug in to quadratic formula and based on answer choices, 4 fulfills the situation. So looking at original setup, each student originally paid $5 and so there were 20 students. Now, with 5 more students, each pays $4.

So, the answer is 25 students, $4 each

x = -b +/-

Answer 2

100/x - 1 = 100/(x+5)

multiply by x(x+5)

100(x+5) - x(x+5) = 100x

100x + 500 -x^2 -5x = 100x

x^2 +5x -500 =0

(x+25)(x-20) = 0

x = 20

x+5 = 25 students involved

they each paid 100/25 = $4

originally they had planned to pay 100/20 = $5