document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95592>Question 95592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69634 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=69634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. 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?<BR>\n" );
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document.write( "Let the original square have x rows and x columns<BR>\n" );
document.write( "It then has x^2 characters in it and 24 left out.\r<BR>\n" );
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document.write( "The modified square has (x+1) rows and (x+1) columns.<BR>\n" );
document.write( "It then has room for (x+1)(x+1) characters  but 25 spots<BR>\n" );
document.write( "are empty.<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "The number of characters has not changed so:<BR>\n" );
document.write( "# in original square + 24 = # in modified square -25<BR>\n" );
document.write( "x^2+24 = (x+1)^2-25<BR>\n" );
document.write( "x^2+24 = x^2+2x-24<BR>\n" );
document.write( "2x = 48<BR>\n" );
document.write( "x = 24<BR>\n" );
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document.write( "So, how many characters are there?<BR>\n" );
document.write( "x^2+24 =  600 characters<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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