document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204421>Question 1204421</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cynthia Besch wants to buy a rug for a room that is  27ft wide and  35ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 609 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 #840663 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=840663\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You have received several responses showing different formal solutions, or showing links to where you can see a solution.<br><BR>\n" );
document.write( "In a situation where finding the solution quickly is important and a formal algebraic solution is not required, there are much faster paths to the solution than formal algebra.<br><BR>\n" );
document.write( "The difference between the dimensions of the room is 8 feet.  So the solution will be two numbers whose difference is 8 and whose product is 609.<br><BR>\n" );
document.write( "With no algebra at all, you can solve the problem simply with mental arithmetic to find those two numbers.<br><BR>\n" );
document.write( "609 = 3(203) = 3(7)(29) = (21)(29)<br><BR>\n" );
document.write( "ANSWERS: 21 feet and 29 feet<br><BR>\n" );
document.write( "There is also a quick algebraic shortcut that can get you to the solution after determining that you need two numbers whose difference is 8 and whose product is 609.<br><BR>\n" );
document.write( "Given the difference of 8 between the two numbers, let the two numbers be x+4 and x-4.  Then, since the product is 609,<br><BR>\n" );
document.write( "(x+4)(x-4) = 609<BR>\n" );
document.write( "x^2-16 = 609<BR>\n" );
document.write( "x^2 = 625<BR>\n" );
document.write( "x = 25<br><BR>\n" );
document.write( "And again the two dimensions are 25+4 = 29 feet and 25-4 = 21 feet.<br><BR>\n" );
document.write( " </SPAN>\n" );
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