document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124151>Question 1124151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Bob's family room is 13 ft by 16 ft, and they want to carpet it, except for a border of uniform width. What would be the width of the border if they can afford only 108 sq ft of carpet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740520 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=740520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 13 by 16 = 208 square feet.<BR>\n" );
document.write( "that's the area of the room.<BR>\n" );
document.write( "let x equal the width of the border all around.\r<BR>\n" );
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document.write( "the width of the carpet will be 13 - 2x<BR>\n" );
document.write( "the length of the carpet will be 16 - 2x.\r<BR>\n" );
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document.write( "the area of the carpet is 108 square feet.\r<BR>\n" );
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document.write( "therefore (13 - 2x) * (16 - 2x) = 108\r<BR>\n" );
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document.write( "simplify to get 13 * 16 - 13 * 2x - 2x * 16 - 2x * -2x\r<BR>\n" );
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document.write( "combine like terms to get 208 - 58x + 4x^2 = 108\r<BR>\n" );
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document.write( "subtract 108 from both sides of the equation to get 100 - 58x + 4x^2 = 0\r<BR>\n" );
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document.write( "reorder the terms in descending order of degree to get 4x^2 - 58x + 100 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get x = 12.5 or x = 2.\r<BR>\n" );
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document.write( "x can't be 12.5 because 13 - 2x would be negative.\r<BR>\n" );
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document.write( "therefore x has to be equal to 2 or not at all.\r<BR>\n" );
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document.write( "when x = 2, you get (13 - 4) * ( 16 - 4) becomes 9 * 12 = 108.\r<BR>\n" );
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document.write( "the area of the rug is 108 square feet.\r<BR>\n" );
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document.write( "the area of the room is (9+4) * (12+4) = 13 * 16 = 208.\r<BR>\n" );
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document.write( "the width of the border all around will be 2 feet.\r<BR>\n" );
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document.write( "the area of the border all around should be 100 square feet.\r<BR>\n" );
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document.write( "along the length you get 16 * 2 = 32 * 2 = 64 square feet.\r<BR>\n" );
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document.write( "along the width you get 13 * 2 = 26 * 2 = 52 square feet.\r<BR>\n" );
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document.write( "total them up and you get 116 square feet.\r<BR>\n" );
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document.write( "the 4 corners of the room have been double counted.\r<BR>\n" );
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document.write( "therefore you have to subtract 4 * (2 * 2) = 4 * 4 = 16 square feet.\r<BR>\n" );
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document.write( "116 square feet minus 16 square feet = 100 square feet for the area of the border all around.\r<BR>\n" );
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document.write( "it all checks out.\r<BR>\n" );
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document.write( "your solution is that the width of the border is 2 feet.\r<BR>\n" );
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document.write( "here's my diagram.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/092403.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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