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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.

Guest Feb 22, 2019

edited by
Guest
Feb 22, 2019

edited by Guest Feb 22, 2019

edited by Guest Feb 22, 2019

#1**+3 **

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

CPhill Feb 22, 2019