Question

a group of friends shared the expenses of an automobile trip,which cost $40.if there had been 3 more people in the group.each would have $3 less.how many people were there in the group and how much did each pay?

Answer 1

let the number of people in the original group be n
then the cost/person = 40/n

new group = n+3
cost per person in new group = 40/n - 3

but (40/n - 3)(n + 3) = 40
expanding, multiplying each term by n and simplifying gave me
n^2 + 3n - 40 = 0
(n+8)(n-3) = 0
n = -8 or n = 5
(can't have negative number of people, so
n = 5

there were 5 people in the original group and each paid $8