document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151693>Question 1151693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . A cabinet has two sliding doors of different sizes. When the cabinet is fully closed,<BR>\n" );
document.write( "they overlap by two-fifths of the width of the smaller door. When both doors are<BR>\n" );
document.write( "slid to one side, the part of the longer door that is not behind the shorter one is <BR>\n" );
document.write( "half as wide as the original overlap, and the open portion of the cabinet is 36<BR>\n" );
document.write( "inches wide. What is the width of the whole cabinet?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773527 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=773527\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let T = the total width of the cabinet.<BR>\n" );
document.write( "let S equal the length of the shorter door.<BR>\n" );
document.write( "let L equal the length of the longer door.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when the doors are shut, then the overlap is 2/5 * S.<BR>\n" );
document.write( "therefore T = S + L - 2/5 * S.<BR>\n" );
document.write( "this makes T = 3/5 * S + L\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when the doors are open, T = L + 36\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since T = L + 36 and T = 3/5 * S + L, then:<BR>\n" );
document.write( "L + 36 = 3/5 * S + L<BR>\n" );
document.write( "subtract L from both sides of this equation to get:<BR>\n" );
document.write( "36 = 3/5 * S<BR>\n" );
document.write( "solve for S to get:<BR>\n" );
document.write( "S = 5/3 * 36 = 60\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when the doors are open, you also get L = S + 1/5 * S.<BR>\n" );
document.write( "since S = 60, this means that L = 60 + 12 = 72\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you now have S = 60 and L = 72<BR>\n" );
document.write( "when the doors are closed, you get T = S + L - 2/5 * S<BR>\n" );
document.write( "this becomes T = 60 + 72 - 24.<BR>\n" );
document.write( "this makes T = 108\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when the doors are open, you get T = L + 36.<BR>\n" );
document.write( "since L = 72, this becomes T = 72 + 36<BR>\n" );
document.write( "this makes T = 108.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when the doors are open, you get T = S + 1/5 * S + 36<BR>\n" );
document.write( "since S = 60, this becomes T = 60 + 12 + 36.<BR>\n" );
document.write( "this makes T = 108\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the numbers check out.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the length of the shorter door is 60 inches.<BR>\n" );
document.write( "the length of the longer door is 72 inches.<BR>\n" );
document.write( "the length of the cabinet is 108 inches.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can be visualized in the following display.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/012702.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the very top line that is not labeled was an error and should be ignored.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your solution is that the length of the cabinet is 108 inches.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );