document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=722233>Question 722233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 85cm long rod is cut into 3 pieces. The longest piece is 3 times as long as the shortest piece and 13 cm longer than the remaining piece. What is the length of the longest piece? \r<BR>\n" );
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document.write( "Please help! I dont know how to do the question but the answer is in the back of the book! My teacher didnt have time to explain how to do these types of questions<BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #442690 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=442690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Don't try to remember questions - remember solution techniques.<BR>\n" );
document.write( "Always define variables to represent the unknowns. Set up equations to fit the problem statement. Then solve the equations.<BR>\n" );
document.write( "Let s = the shortest piece<BR>\n" );
document.write( "Let L = the longest piece<BR>\n" );
document.write( "Let r = the remaining piece<BR>\n" );
document.write( "What do we know?<BR>\n" );
document.write( "1) the three pieces add up to 85<BR>\n" );
document.write( "2) L = 3*s<BR>\n" );
document.write( "3) L = r + 13<BR>\n" );
document.write( "Start with the basis of this type of problem that \"the whole is equal to the sum of its parts\" and get<BR>\n" );
document.write( "(1) s + L + r = 85<BR>\n" );
document.write( "We can eliminate r by using fact 3) and get<BR>\n" );
document.write( "(2) r = L - 13.<BR>\n" );
document.write( "Substitute r of (2) into (1) and get<BR>\n" );
document.write( "(3) s + L + (L - 13) = 85 or<BR>\n" );
document.write( "(4) s + 2*L = 85 + 13 or<BR>\n" );
document.write( "(5) s + 2*L = 98<BR>\n" );
document.write( "Now apply fact 2) to get<BR>\n" );
document.write( "(6) s + 2*(3*s) = 98 or<BR>\n" );
document.write( "(7) s + 6*s = 98 or<BR>\n" );
document.write( "(8) 7*s = 98 or<BR>\n" );
document.write( "(9) s = 14<BR>\n" );
document.write( "Then from fact 2) we get<BR>\n" );
document.write( "(10) L = 3*14 or<BR>\n" );
document.write( "(11) L = 42 and<BR>\n" );
document.write( "from (2) we get<BR>\n" );
document.write( "(12) r = 42 - 13 or<BR>\n" );
document.write( "(13) r = 29<BR>\n" );
document.write( "Let's check using with (1).<BR>\n" );
document.write( "Is (14 + 42 + 29 = 85)?<BR>\n" );
document.write( "Is (85 = 85)? Yes<BR>\n" );
document.write( "Answer: The longest piece is 42 cm.<BR>\n" );
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