Question 69720: Question: "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?"
Gracias!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Question: "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 1st square have x rows and x columns.
Then # of characters is x^2+24
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The 2nd square has (x+1) rows and (x+1) columns.
Then # of characters is (x+1)(x+1)-25
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Since the # of characters has not changed:
EQUATION:
x^2+24=(x+1)(x+1)-25
x^2+24 = x^2+2x-24
2x=48
x=24 (# of rows and # of columns in the 1st square)
# of characters = x^2+24= 24^2+24=600
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Cheers,
Stan H.
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