Question 132826: 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 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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