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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.

 Feb 22, 2019
edited by Guest  Feb 22, 2019
edited by Guest  Feb 22, 2019
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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

 

 

cool cool cool

 Feb 22, 2019

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