document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196090>Question 1196090</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 30 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 476 square feet of carpeting. What dimensions should the rug ​have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828795 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=828795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The difference between the length and width of the room is 30-19=11 feet.  Since the strip around the rug is to be of uniform width, the difference between the length and width of the rug must also be 11 feet.<br><BR>\n" );
document.write( "So find how to factor 476 as the product of two integers whose difference is 11.<br><BR>\n" );
document.write( "476 = 119*4 = 7*17*4 = 28*17<br><BR>\n" );
document.write( "ANSWER: The rug should be 28 feet long and 17 feet wide.<br><BR>\n" );
document.write( "For a formal algebraic solution, we can let x be the width of the uniform strip around the rug, making the dimensions of the rug 30-2x and 19-2x.  Then, given the area of the rug as 476 square feet,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830-2x%29%2819-2x%29=476 ALIGN=MIDDLE  ALT=\"%2830-2x%29%2819-2x%29=476\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=570-98x%2B4x%5E2=476 ALIGN=MIDDLE  ALT=\"570-98x%2B4x%5E2=476\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-98x%2B94=0 ALIGN=MIDDLE  ALT=\"4x%5E2-98x%2B94=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-49x%2B47=0 ALIGN=MIDDLE  ALT=\"2x%5E2-49x%2B47=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-47%29%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%282x-47%29%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The width of the uniform strip is either 47/2 = 23.5 feet or 1 foot.<br><BR>\n" );
document.write( "The 23.5 feet makes no sense, so the width of the strip is 1 foot, making the dimensions of the rug 28 feet by 17 feet.<br><BR>\n" );
document.write( "But that algebraic solution was much harder than the informal solution shown earlier -- so the formal algebra doesn't give you an easier way to find the answer to the problem.<br><BR>\n" );
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