Let n be the number of friends originally in the group. Since the cost of the trip was 800 dollars, the share, in dollars, for each friend was originally
.When two friends decided not to go on the trip, the number of friends who split the 800 dollars cost became
n−2, and each friend’s cost became
. Since this share represented a 20 dollars increase over the original share, the equation
+20= must be true. Multiplying each side of
+20= by
n(n−2) to clear all the denominators gives.
800(n−2)+20n(n−2)=80nThis is a quadratic equation and can be rewritten in the standard form by expanding,simplifying, and then collecting like terms on one side, as shown below:
800n+1600+20n2−40n=800n
40n−80+n2−2n=40n
n2−2n−80=0After factoring, this becomes
(n+8)(n−10)=0.The solutions of this equation are −8 and 10. Since a negative solution makes no sense for thenumber of people in a group, the number of friends originally in the group was 10.