document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162695>Question 1162695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am needing help in setting up this equation:<BR>\n" );
document.write( "A 96 ft rope is cut into 4 pieces. The second piece is 6 less than twice as long as the first piece. The third piece is 5 feet greater than the first piece. AndThe fourth is half as long as the second piece. How long is the fourth piece? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786519 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=786519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the length of each piece be a, b, c, d.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "a + b + c + d = 96<BR>\n" );
document.write( "you get the following additional equations based on the problem statement.<BR>\n" );
document.write( "b = 2a - 6<BR>\n" );
document.write( "c = a + 5<BR>\n" );
document.write( "d = b/2<BR>\n" );
document.write( "the trick is to reduce the number of variables to 1.<BR>\n" );
document.write( "then the problem can be solved.<BR>\n" );
document.write( "we'll try to make everything in terms of a.<BR>\n" );
document.write( "d = b/2 is not in terms of a, but we know that b = 2a - 6<BR>\n" );
document.write( "replace b in the equation of d = b/2 to get d = (2a - 6) / 2<BR>\n" );
document.write( "now you have everything in terms of a.<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "b = 2a - 6<BR>\n" );
document.write( "c = a + 5<BR>\n" );
document.write( "d = (2a - 6) / 2<BR>\n" );
document.write( "a + b + c + d = 96 becomes:<BR>\n" );
document.write( "a + (2a - 6) + (a + 5) + (2a - 6) / 2 = 96<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "a + 2a - 6 + a + 5 + 2a/2 - 6/2 = 96<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "a + 2a - 6 + a + 5 + a - 3 = 96<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "5a - 4 = 96<BR>\n" );
document.write( "add 4 to both sides of the equation to get:<BR>\n" );
document.write( "5a = 100<BR>\n" );
document.write( "solve for a to get:<BR>\n" );
document.write( "a = 100 / 5 = 20<BR>\n" );
document.write( "b = 2a - 6 = 40 - 6 = 34<BR>\n" );
document.write( "c = a + 5 = 25<BR>\n" );
document.write( "d = b / 2 = 17<BR>\n" );
document.write( "a + b + c + d = 20 + 34 + 25 + 17 = 96<BR>\n" );
document.write( "solution is confirmed to be good.<BR>\n" );
document.write( "solution is the fourth piece (piece d) is 17 feet in length.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );