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

Question 58875: 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?
This is what I have..Let x=original number of rows of the square grid. Since number of rows and columns are equal, then number of columns is x also. So the original area, or original number of characters of the square, is x^2. Also, 24 characters were left out, so first set up the expression for total number of characters based on this. Also, when he added one more row and column, making each x+1 now, the new area is (x+1)^2 and is short 25 characters. So get a new expression for the number of characters. Set the two expressions equal since each represents the total number of characters. Solve for x.
Answer by 303795(602) (Show Source): You can put this solution on YOUR website!

x=24
So the original shape had 24*24+24=600 and the enlarged shape had 25*25-25=600 characters as well

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