If $480 is divided equally among N people, each person will get $x each. If two more people are added to the group, each person gets $(x - 20). Which of the following is N?
(A) 4
(B) 6
(C) 7
(D) 8
(E) 9
Explanation:
If $480 is equally divided among N people and they get x dollars each, then 480/N = x
If two more people are added, then the total number of people increases to N + 2.
Hence, each person now gets $480/(N + 2).
This is given to be x - 20. So, 480/(N + 2) = x - 20
So, we have that 480/N = x and 480/(N + 2) = x - 20.
Subtracting the two equations, we get
480/N - 480/(N + 2) = x - (x - 20) = 20
24/N - 24/(N + 2) = 1 Þ24(N + 2) - 24N = N(N + 2)
48 = N2 + 2N or N2 + 2N - 48 = 0
So, (N + 8)(N - 6) = 0 implies N = -8 or N = 6.
Since the number of people cannot be negative, N = -8 is rejected and we only take the value N = 6.
The correct answer is B.
http://www.gurome.com/Blog
it's a smart analyse equation charbel. but is it an application of linear algebra?
ReplyDelete