document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113179>Question 1113179</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cynthia Besch wants to buy a rug for a room that is 23 ft wide and 30 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 408<BR>\n" );
document.write( "square feet of carpeting. What dimensions should the rug&#8203; have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728181 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=728181\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the distance between the rug and the walls be x on all sides.\r<BR>\n" );
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document.write( "the area of the room is 30 * 23 = 690\r<BR>\n" );
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document.write( "the area of the rug is (30 - 2x) * (23 - 2x) = 408\r<BR>\n" );
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document.write( "perform the multiplication to get:\r<BR>\n" );
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document.write( "690 - 60x - 46x + 4x^2 = 408\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "690 - 106x + 4x^2 = 408\r<BR>\n" );
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document.write( "subtract 408 from both sides of the equation to get:\r<BR>\n" );
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document.write( "690 - 106x + 4x^2 - 408 = 0\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "282 - 106x + 4x^2 = 0\r<BR>\n" );
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document.write( "reorder the terms in descending order of degree to get:\r<BR>\n" );
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document.write( "4x^2 - 106x + 282 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get:\r<BR>\n" );
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document.write( "x = 23.5 or x = 3\r<BR>\n" );
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document.write( "x can't be 23.5 because then the area of the rug would not be equal to 408 because:\r<BR>\n" );
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document.write( "(30 - 2 * 23.5) * (23 - 2 * 23.5) equals a negative.\r<BR>\n" );
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document.write( "x has to be 3 or none of the possible solutions are good.\r<BR>\n" );
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document.write( "when x = 3, you get (30 - 6) * (23 - 6) = 408.\r<BR>\n" );
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document.write( "this results in 24 * 17 = 408 which becomes 408 = 408 which is true.\r<BR>\n" );
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document.write( "your solution is that x = 3 and the dimensions of the rug are 24 by 17.\r<BR>\n" );
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document.write( "this rug fits into a room that is 30 by 23.\r<BR>\n" );
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document.write( "there will be a border around the rug that is 3 feet in all directions.\r<BR>\n" );
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document.write( "the dimensions of the room are 30 by 23\r<BR>\n" );
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document.write( "the dimensions of the rug are 24 by 17.\r<BR>\n" );
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document.write( "the difference between the length of the room and the length of the rug is 30 - 24 = 6.\r<BR>\n" );
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document.write( "the difference between the width of the room and the width of the rug is 23 17 = 6.\r<BR>\n" );
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document.write( "divide this difference by 2 and you get 3 foot border between the rug and the wall all around.\r<BR>\n" );
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document.write( "here's my picture.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/032501.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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