Question 200499
A square grid tells us that the dimensions are n x n. So the total area of the square grid is {{{n^2}}}. Since 24 characters were left out, this means that the total number of characters are {{{n^2+24}}}. 



Since the designer added one "one more row and column", this makes the new area {{{(n+1)^2}}}. Since he was short 25 characters, this means that the expression then becomes {{{(n+1)^2-25}}}



{{{(n+1)^2-25=n^2+24}}} Now set the two expressions equal to one another



{{{n^2+2n+1-25=n^2+24}}} FOIL



{{{n^2+2n+1-25-n^2-24=0}}} Subtract {{{n^2}}} from both sides. Subtract {{{24}}} from both sides.



{{{2n-48=0}}} Combine like terms.



{{{2n=0+48}}} Add {{{48}}} to both sides.



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



{{{n=(48)/(2)}}} Divide both sides by {{{2}}} to isolate {{{n}}}.



{{{n=24}}} Reduce.



{{{n^2+24}}} Now go back to the first expression



{{{24^2+24}}} Plug in {{{n=24}}}



{{{600}}} Simplify



So the designer used 600 characters.




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