SOLUTION: A designer, attemptng 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
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Question 94569: A designer, attemptng 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 ankor@dixie-net.com(22740) (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?
:
Let x^2 = no. of characters in the original square
:
Then the total number of characters = x^2 + 24
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Add one column and row and you have (x+1)^2 in the new square
:
Original square + 24 = new square - 25
x^2 + 24 = (x+1)^2 - 25
x^2 + 24 = x^2 + 2x + 1 - 25
:
Arrange the unknowns on the left and the numerals on the right:
x^2 - x^2 - 2x = 1 - 25 - 24
-2x = - 48
x = -48/-2
x = +24
:
The number of characters = x^2 + 24
24^2 + 24
576 + 24 = 600 characters used by the designer
:
Check by using the new square
25^2 - 25
625 - 25 = 600 also
:
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