document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200499>Question 200499</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150763 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=150763\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A square grid tells us that the dimensions are n x n. So the total area of the square grid is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since 24 characters were left out, this means that the total number of characters are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B24 ALIGN=MIDDLE  ALT=\"n%5E2%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Since the designer added one \"one more row and column\", this makes the new area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"%28n%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since he was short 25 characters, this means that the expression then becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%5E2-25 ALIGN=MIDDLE  ALT=\"%28n%2B1%29%5E2-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%5E2-25=n%5E2%2B24 ALIGN=MIDDLE  ALT=\"%28n%2B1%29%5E2-25=n%5E2%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now set the two expressions equal to one another\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n%2B1-25=n%5E2%2B24 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n%2B1-25=n%5E2%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n%2B1-25-n%5E2-24=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n%2B1-25-n%5E2-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides. Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n-48=0 ALIGN=MIDDLE  ALT=\"2n-48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n=0%2B48 ALIGN=MIDDLE  ALT=\"2n=0%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n=48 ALIGN=MIDDLE  ALT=\"2n=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%2848%29%2F%282%29 ALIGN=MIDDLE  ALT=\"n=%2848%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=24 ALIGN=MIDDLE  ALT=\"n=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B24 ALIGN=MIDDLE  ALT=\"n%5E2%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now go back to the first expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%5E2%2B24 ALIGN=MIDDLE  ALT=\"24%5E2%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=24 ALIGN=MIDDLE  ALT=\"n=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600 ALIGN=MIDDLE  ALT=\"600\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So the designer used 600 characters.\r<BR>\n" );
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document.write( "If you have any questions, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com\">jim_thompson5910@hotmail.com</a>.<BR>\n" );
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