Question 22156: Good Evening, I am having a hard time answering this question. I don't even know how to set it up. Please help.
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(75887)   (Show Source):
You can put this solution on YOUR website! We don't know the dimensions of the 1st square so let it be length=x and width =x. This square can accomodate x^2 of the "characters". But 24 are left over
so there must be x^2+ 24 characters.
The 2nd square has had a row and a column added so its length=x+1 and its width =x+1. This 2nd square can accomodate (x+1)^2 characters. But there
are then 25 positions in the square that have no character. Thus the total
number of characters must be (x+1)^2-25.
Since there are the same number of characters described in the two scenarios
the following equation must apply:
x^2 + 24 = (x+1)^2-25
Solve this equation for "x".
Then the number of characters is x^2+24 or (x+1)^2 -25.
Both give the same number if you have correctly solved for "x".
Good luck,
Cheers,
Stan H.
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