Question 95592: 1. 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?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. 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 square have x rows and x columns
It then has x^2 characters in it and 24 left out.
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The modified square has (x+1) rows and (x+1) columns.
It then has room for (x+1)(x+1) characters but 25 spots
are empty.
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EQUATION:
The number of characters has not changed so:
# in original square + 24 = # in modified square -25
x^2+24 = (x+1)^2-25
x^2+24 = x^2+2x-24
2x = 48
x = 24
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So, how many characters are there?
x^2+24 = 600 characters
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Cheers,
Stan H.
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