SOLUTION: Hi everyone...this is one im stuck on. 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

Question 205919: Hi everyone...this is one im stuck on.
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?
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) (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?
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Original pattern: # of characters = x^2+24
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New pattern: # of characters = (x+1)^2-25
===============================================
Equation:
x^2+24 = (x+1)^2-25
x^2 + 24 = x^2 + 2x + 1 - 25
2x-24 = 24
2x = 48
x = 24
---
# of characters = x^2+24 = 24^2+24 = 600
==============================================
Cheers,
Stan H.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Try this!
Let x = the number of characters in his first square. Since he had 24 characters left over, then this can be expressed as:

Now when he tried to add one more row and column, he was short 25 characters, and this can be expressd as:
and these two amounts are the same, so...
Simplify and solve for x.

Subtract from both sides.
Add 24 to both sides.
Divide both sides by 2.

So, now we substitute this value of x into the first (or second) equation to find the original number of characters he started with.
=
The designer used 600 characters.
Check:
First try:
=
Second try:
=

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