SOLUTION: when a regiment is arranged in a perfect square,the number of soldiers in the front row is 15 less than the number of soldiers in front row arranged in 4 deep hollow square.find th

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Question 925216: when a regiment is arranged in a perfect square,the number of soldiers in the front row is 15 less than the number of soldiers in front row arranged in 4 deep hollow square.find the number of soldiers?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
when a regiment is arranged in a perfect square,the number of soldiers in the front row is 15 less than the number of soldiers in front row arranged in 4 deep hollow square. find the number of soldiers?
"Hollow square" means a rectangle. (I had to look that up)

So let n = the number of soldiers in the front row when arranged in a
hollow square

The the total number of soldiers is 4n

The number in the front row when arranged in a perfect square is n-16.

Then the total number of soldiers is (n-15)2.

We form the equation by setting the two equal:

4n = (n-15)2
4n = (n-15)(n-15)
4n = n2-15n-15n+225
4n = n2-30n+225
 0 = n2-34n+225
 0 = (n-25)(n-9)

     n-25=0;  n-9=0
        n=25;   n=9
Two solutions, but 9 does not work 
since n-16 would be negative.

The number of soldiers is 100.

Edwin
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