document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314933>Question 314933</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 16 ft by 24 ft and the area of the rug is 153 sqft, how wide will the border be? <BR>\n" );
document.write( "a=w*l, a=16*24 = 384 ft ?<BR>\n" );
document.write( "wouldn't you just subtract the 153 from the 384, then divide by four? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225262 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=225262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 16 ft by 24 ft and the area of the rug is 153 sqft, how wide will the border be? <BR>\n" );
document.write( "a=w*l, a=16*24 = 384 ft ?<BR>\n" );
document.write( "wouldn't you just subtract the 153 from the 384, then divide by four?\"\r<BR>\n" );
document.write( "\n" );
document.write( "room is 16 ft by 24 ft<BR>\n" );
document.write( "room area = 16 * 24 = 384 square feet<BR>\n" );
document.write( "rug area = 153 square feet<BR>\n" );
document.write( "area border = room area - rug area<BR>\n" );
document.write( "area border = 384 - 153 = 231 square feet<BR>\n" );
document.write( "area border = w * 16 + w * 16 + w(24 - 2w) + w(24 - 2w) = 231<BR>\n" );
document.write( "area border = 32w + 24w - 2w^2 + 24w - 2w^2 = 231<BR>\n" );
document.write( "area border = 32w + 48w - 4w^2 = 231<BR>\n" );
document.write( "-4w^2 + 80w - 231 = 0<BR>\n" );
document.write( "  w^2 - 20w + 57.75 = 0<BR>\n" );
document.write( "a = 1, b = -20, c = 57.75<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%2820+%2B-+sqrt%28+400+-+4%2857.75%29+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w+=+%2820+%2B-+sqrt%28+400+-+4%2857.75%29+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%2820+%2B-+sqrt%28400+-+231%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w+=+%2820+%2B-+sqrt%28400+-+231%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%2820+%2B-+sqrt%28169%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w+=+%2820+%2B-+sqrt%28169%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%2820+%2B-+13%29%2F2+ ALIGN=MIDDLE  ALT=\"w+=+%2820+%2B-+13%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "w1 = (20 + 13)/2 = 33/2 = 16.5, which makes no sense<BR>\n" );
document.write( "w2 = (20 - 13)/2 = 7/2 = 3.5, so border width is 3.5<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "2 * (3.5*16) + 2 * (3.5 * (24-7))<BR>\n" );
document.write( "2 * 56 + 2 * (3.5 * 17)<BR>\n" );
document.write( "112 + 2(59.5)<BR>\n" );
document.write( "112 + 119<BR>\n" );
document.write( "231<BR>\n" );
document.write( "(dividing 231 by 4, would give you 57.75)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );