document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1017802>Question 1017802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A stick 46 metres long is divided into two parts so that 2/5 of one part is equal to 3/4 of the other part. Find the lengths of the two pieces. [ Let the length of one part be x m, then the other length is (46-x)m] I've been struggling with this for more than 20 minutes, so I'm just wondering if you could help, thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634048 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=634048\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let one part be equal to x and let the other part be equal to y.\r<BR>\n" );
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document.write( "x + y = 46.\r<BR>\n" );
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document.write( "you are given that 2/5 * the first part is equal to 3/4 of the other part.\r<BR>\n" );
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document.write( "the equation for that becomes 2/5 * x = 3/4 * y\r<BR>\n" );
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document.write( "to simplify further operations, multiply both sides of this equation by 20 to get:\r<BR>\n" );
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document.write( "2/5 * 20 * x = 3/4 * 20 * y\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "8 * x = 15 * y.\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "x + y = 46\r<BR>\n" );
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document.write( "8x = 15y\r<BR>\n" );
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document.write( "solve for y in the first equation to get y = 46 - x.\r<BR>\n" );
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document.write( "replace y in the second equation with 46 - x to get:\r<BR>\n" );
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document.write( "8x = 15 * (46 - x)\r<BR>\n" );
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document.write( "distribute the multiplication on the right side of the equation to get:\r<BR>\n" );
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document.write( "8x = 15 * 46 - 15x\r<BR>\n" );
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document.write( "simplify to get 8x = 690 - 15x\r<BR>\n" );
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document.write( "add 15x to both sides of the equation to get:\r<BR>\n" );
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document.write( "8x + 15x = 690 - 15x + 15x becomes:\r<BR>\n" );
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document.write( "23x = 690\r<BR>\n" );
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document.write( "divide both sides of the equation by 23 to get:\r<BR>\n" );
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document.write( "x = 690 / 23 = 30.\r<BR>\n" );
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document.write( "since x + y = 46, this means that y must be equal to 16.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = 30<BR>\n" );
document.write( "y = 16\r<BR>\n" );
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document.write( "x + y = 30 + 16 = 46\r<BR>\n" );
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document.write( "8x = 15y becomes 8*30 = 15*16 which becomes 240 = 240.\r<BR>\n" );
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document.write( "this confirms the solution is good.\r<BR>\n" );
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document.write( "as further confirmation, you want to have 2/5 * x = 3/4 * y.\r<BR>\n" );
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document.write( "this becomes 2/5 * 30 = 3/4 * 16.\r<BR>\n" );
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document.write( "this becomes 60/5 = 48/4 which becomes 12 = 12.\r<BR>\n" );
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document.write( "your confirmation is final and your solution is good.\r<BR>\n" );
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document.write( "x = 30 and y = 16.\r<BR>\n" );
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document.write( "one part of the stick measures 30 meters and the other part of the stick measure 16 meters.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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