math

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?

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  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

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