Quadratic equation a 44

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.

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