SAT Mathematics Practice Test 6

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 $\frac{800}{n}$.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 $\frac{800}{n-2}$ . Since this share represented a 20 dollars increase over the original share, the equation $\frac{800}{n}+20=\frac{800}{n-2}$ must be true. Multiplying each side of $\frac{800}{n}+20=\frac{800}{n-2}$ by$n(n-2)$ to clear all the denominators gives.$800(n-2)+20n(n-2)=80n$This 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:$800n+1600+20n^2-40n=800n$

$40n-80+n^2-2n=40n$

$n^2-2n-80=0$After 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.