SOLUTION: A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of rows and columns, found that 24 characters were left out. When he

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Question 95400: A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of rows and columns, found that 24 characters were left out. When he tried to add one more row and column, he found that he was short of 25 characters. Can you find the number of characters used by the designer?
*note* I really would like some help as to how to setup this question. Thank you!
Answer by stanbon(57288) About Me  (Show Source):
You can put this solution on YOUR website!
A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of rows and columns, found that 24 characters were left out. When he tried to add one more row and column, he found that he was short of 25 characters. Can you find the number of characters used by the designer?
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Let the original number of rows and columns be "x"
Then the number of characters is x^2+24
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When he added a row and a column the square was (x+1)*(x+1)
but the number of characters was still the same.
So he had (x+1)^2-25.
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EQUATION:
original # of charactres = new number of characters
x^2+24 = (x+1)^2-25
x^2+24 = x^2+2x+1-25
24 = 2x-24
2x = 48
x= 24 (this is the original # of rows and columns)
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# of characters = x^2+24
= 600
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Notice (24+1)^2-25 also equals 600
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Cheers,
Stan H.