document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=261793>Question 261793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 139 m. rope is cut into 3 pieces. One piece is 30 m. more then half the shortest piece. The third piece is twice the sum of the length of the shortest piece and 2. What are the lengths of the pieces? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #192935 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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=192935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Total length = 139m<BR>\n" );
document.write( "there are 3 pieces of rope<BR>\n" );
document.write( "Setup:<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Notice that each length is given in respect to the shotest piece.<BR>\n" );
document.write( "Let A = the length of the shortest piece<BR>\n" );
document.write( "Let B = the length of the second piece<BR>\n" );
document.write( "Let C = the length of the third piece<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+A%2F2+%2B+30 ALIGN=MIDDLE  ALT=\"B+=+A%2F2+%2B+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+2%2A%28A%2BB%29 ALIGN=MIDDLE  ALT=\"C+=+2%2A%28A%2BB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+B+%2B+C+=+139 ALIGN=MIDDLE  ALT=\"A+%2B+B+%2B+C+=+139\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solution:<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Since we know what B and C equal in terms of A, we can substitute the values into equation 3<BR>\n" );
document.write( "Equation 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+B+%2B+C+=+139 ALIGN=MIDDLE  ALT=\"A+%2B+B+%2B+C+=+139\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+%28A%2F2+%2B+30%29+%2B+2%2A%28A%2BB%29+=+139 ALIGN=MIDDLE  ALT=\"A+%2B+%28A%2F2+%2B+30%29+%2B+2%2A%28A%2BB%29+=+139\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+%28A%2F2+%2B+30%29+%2B+2%2A%28A+%2B+%28A%2F2+%2B+30%29%29+=+139 ALIGN=MIDDLE  ALT=\"A+%2B+%28A%2F2+%2B+30%29+%2B+2%2A%28A+%2B+%28A%2F2+%2B+30%29%29+=+139\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+A%2F2+%2B+30+%2B+2A+%2B+2A%2F2+%2B+60%29+=+139 ALIGN=MIDDLE  ALT=\"A+%2B+A%2F2+%2B+30+%2B+2A+%2B+2A%2F2+%2B+60%29+=+139\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+A%2F2+%2B+30+%2B+2A+%2B+A+%2B+60+=+139 ALIGN=MIDDLE  ALT=\"A+%2B+A%2F2+%2B+30+%2B+2A+%2B+A+%2B+60+=+139\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.5A+%2B+90+=+139 ALIGN=MIDDLE  ALT=\"4.5A+%2B+90+=+139\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 90 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.5A+=+49 ALIGN=MIDDLE  ALT=\"4.5A+=+49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 4.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A+=+10.89%29 ALIGN=MIDDLE  ALT=\"highlight%28A+=+10.89%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*Rounded\r<BR>\n" );
document.write( "\n" );
document.write( "Now we can find the other lengths by replacing A with 10.89 in equations 1 & 2<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+A%2F2+%2B+30 ALIGN=MIDDLE  ALT=\"B+=+A%2F2+%2B+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+10.89%2F2+%2B+30 ALIGN=MIDDLE  ALT=\"B+=+10.89%2F2+%2B+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B+=+35.45%29 ALIGN=MIDDLE  ALT=\"highlight%28B+=+35.45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*Rounded<BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+2%2A%28A%2BB%29 ALIGN=MIDDLE  ALT=\"C+=+2%2A%28A%2BB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+2%2A%2810.89+%2B+35.45%29 ALIGN=MIDDLE  ALT=\"C+=+2%2A%2810.89+%2B+35.45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C+=+92.68%29 ALIGN=MIDDLE  ALT=\"highlight%28C+=+92.68%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Check the answers:<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "We can check the answers by placing them back into eqaution 3<BR>\n" );
document.write( "Equation 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+B+%2B+C+=+139 ALIGN=MIDDLE  ALT=\"A+%2B+B+%2B+C+=+139\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10.89+%2B+35.45+%2B+92.68+=+139 ALIGN=MIDDLE  ALT=\"10.89+%2B+35.45+%2B+92.68+=+139\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28139.02+=+139%29 ALIGN=MIDDLE  ALT=\"highlight%28139.02+=+139%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Off by .02 due to rounding\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );