document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1071293>Question 1071293</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An 81 inch length of ribbon is to be cut into three pieces. The longest piece is to be 34 inches longer than the shortest piece, and the third piece is to be half the length of the longest piece. Find the length of each piece of ribbon  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #686249 by </B><A HREF=/tutors/aboutme.mpl?userid=Dirichlet><B>Dirichlet(3)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Dirichlet><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=686249\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The ribbon is to be divided into 3 pieces.\r<BR>\n" );
document.write( "\n" );
document.write( "Let:\r<BR>\n" );
document.write( "\n" );
document.write( "l = the length of the longest piece<BR>\n" );
document.write( "s = the length of the shortest piece<BR>\n" );
document.write( "t = the length of the third piece\r<BR>\n" );
document.write( "\n" );
document.write( "So, we get:\r<BR>\n" );
document.write( "\n" );
document.write( "81 = l + s + t\r<BR>\n" );
document.write( "\n" );
document.write( "Given the info that the longest piece is to be 34 inches longer than the shortest piece. The generates the formula:\r<BR>\n" );
document.write( "\n" );
document.write( "l = 34 + s\r<BR>\n" );
document.write( "\n" );
document.write( "Given the info that the third piece is to be half the length of the longest piece. This generates the formula:\r<BR>\n" );
document.write( "\n" );
document.write( "t = l / 2\r<BR>\n" );
document.write( "\n" );
document.write( "Now, we plug l and t into our first formula. We get:\r<BR>\n" );
document.write( "\n" );
document.write( "81 = (34 + s) + s + ((34 + s) / 2)\r<BR>\n" );
document.write( "\n" );
document.write( "Simplifying, we get:\r<BR>\n" );
document.write( "\n" );
document.write( "81 = 51 + 5s/2\r<BR>\n" );
document.write( "\n" );
document.write( "Solving for s, we get s = 12.\r<BR>\n" );
document.write( "\n" );
document.write( "Now, solve for l.\r<BR>\n" );
document.write( "\n" );
document.write( "l = 34 + 12. l = 46.\r<BR>\n" );
document.write( "\n" );
document.write( "Solve for t. t = 46/2. t = 23.\r<BR>\n" );
document.write( "\n" );
document.write( "It checks! 46 + 23 + 12 = 81.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );