SOLUTION: Problem: 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.

Question 132592: Problem: 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?
I don't understand if you are short 24 characters at first and then add another row and column, how can you then be short 25 characters? Maybe it is the wording "short of 25 characters that is throwing me off.
Thanking in advance for any help on this. It is due today and I cannot figure it out and I stayed up until 3:00AM yesterday working on it. Thanks again!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
"24 characters were left out" __ 24 more characters than spaces

"short of 25 characters" __ 25 more spaces than characters

let x="number of rows/columns in original grid", so x+1="number in second grid"
__ let y="number of characters"

"24 characters were left out" __ y=x^2+24

"short of 25 characters" __ y+25=(x+1)^2 __ y+25=x^2+2x+1 __ y=x^2+2x-24

substituting __ x^2+24=x^2+2x-24 __ subtracting x^2-24 __ 48=2x __ 24=x

y=(24)^2+24 __ y=600
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