# 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

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> 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       Log On

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 Question 144621: 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(57962)   (Show Source): You can put this solution on YOUR website!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? ------------------------ EQUATIONS: # of characters = n^2+24 -------- # of characters = (n+1)^2-25 ---------------------- n^2 + 24 = (n+1)^2-25 n^2 + 24 = n^2 + 2n + 1 - 25 2n -24 = 24 2n = 48 n = 24 ----------- # of characters = 24^2+24 = 600 ================= Cheers, Stan H.