A band is marching in a rectangular formation with dimensions n-2 and n+8. In the second stage of their performance, they re-arrange to form a different rectangle with dimensions n and 2n - 3, excluding all the drummers. If there are at least 4 drummers, then find the sum of all possible values of n.
Pls don't show me a graph or anything. I want a step by step explanition so I can understand this, cuz I'm struggling with this unit in school.
+128448 The number of original members = (n - 2) (n + 8)
The reformed number of members is n (2n - 3)
When we take away at least 4 drummers, we have this inequaliy
Original members - Reformed members ≥ 4 ....so....
(n - 2)(n + 8) - n(2n - 3) ≥ 4 simplify
n^2 + 6n - 16 - 2n^2+ 3n ≥ 4
-n^2 + 9n - 20 ≥ 0 multiply through by - 1 and reverse the inequality sign
n^2 - 9n + 20 ≤ 0 factor
(n - 5) ( n - 4) ≤ 0
Note that....this will be > 0 when n < 4 or n > 5
So... the solution must be that 4 ≤ n ≤ 5
So......since n has to be an integer.....the sum of the solutions for n = 4 + 5 = 9
