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 200499: 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 jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A square grid tells us that the dimensions are n x n. So the total area of the square grid is n%5E2. Since 24 characters were left out, this means that the total number of characters are n%5E2%2B24.


Since the designer added one "one more row and column", this makes the new area %28n%2B1%29%5E2. Since he was short 25 characters, this means that the expression then becomes %28n%2B1%29%5E2-25


%28n%2B1%29%5E2-25=n%5E2%2B24 Now set the two expressions equal to one another


n%5E2%2B2n%2B1-25=n%5E2%2B24 FOIL


n%5E2%2B2n%2B1-25-n%5E2-24=0 Subtract n%5E2 from both sides. Subtract 24 from both sides.


2n-48=0 Combine like terms.


2n=0%2B48 Add 48 to both sides.


2n=48 Combine like terms on the right side.


n=%2848%29%2F%282%29 Divide both sides by 2 to isolate n.


n=24 Reduce.


n%5E2%2B24 Now go back to the first expression


24%5E2%2B24 Plug in n=24


600 Simplify


So the designer used 600 characters.



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