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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
