SOLUTION: word problem! 13. A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: word problem! 13. A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters      Log On


   

Question 187214: word problem!
13.
A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer.

I am too confused. I need your help, thanks.
Answer by dukesmart(20) About Me  (Show Source):
You can put this solution on YOUR website!

let put x= number of rows or number of columns
The designer has total characters: x*x +24 = x^2 + 24
If he add 1 row and 1 column then total charcters would be if filled out:
(x+1)(x+1)= x^2+2x+1
total character he has plus 25 empty one ( need to be filled) will be x^2+2x+1
so we can establish the equation as follows:
x^2+24+25 = x^2+2x+1
49 = 2x + 1
48 =2x =======> x=24 rows or 24 columns
Therefore designer has 24*24 +24= 576+24= 600 characters.