document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965193>Question 965193</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a student was walking to school. after going 1 kilometer and half of the rest of the trip, there was still 1 kilometer more than a third of the whole left. how far was the student living  from the school? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589930 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=589930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the length of the trip.\r<BR>\n" );
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document.write( "he traveled 1 kilometer and half of the rest of the trip.\r<BR>\n" );
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document.write( "this is equal to 1 + 1/2 * (x-1).\r<BR>\n" );
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document.write( "there was still 1 kilometer more than a third of the whole left.\r<BR>\n" );
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document.write( "this is equal to 1 + 1/3 * x\r<BR>\n" );
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document.write( "the length of the trip is equal to the length traveled plus the length left to be traveled.\r<BR>\n" );
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document.write( "x is the length of the trip.<BR>\n" );
document.write( "the length traveled is equal to 1 + 1/2 * (x-1)<BR>\n" );
document.write( "the length left to be traveled is equal to 1 + 1/3 * x\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( "x = 1 + 1/2 * (x-1) + 1 + 1/3 * x\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "x = 1 + 1/2 * x - 1/2 + 1 + 1/3 * x\r<BR>\n" );
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document.write( "group like terms to get:\r<BR>\n" );
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document.write( "x = (1 - 1/2 + 1) + (1/2 * x + 1/3 * x)\r<BR>\n" );
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document.write( "convert to common denominators to get:\r<BR>\n" );
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document.write( "x = (2/2 - 1/2 + 2/2) + (3/6 * x + 2/6 * x)\r<BR>\n" );
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document.write( "finish combining like terms to get:\r<BR>\n" );
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document.write( "x = 3/2 + 5/6 * x\r<BR>\n" );
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document.write( "subtract 5/6 * x from both sides of the equation to get:\r<BR>\n" );
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document.write( "x - 5/6 * x = 3/2\r<BR>\n" );
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document.write( "convert to common denominators to get:\r<BR>\n" );
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document.write( "6/6 * x - 5/6 * x = 3/2\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "1/6 * x = 3/2\r<BR>\n" );
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document.write( "multiply both sides of this equation by (6/1) to get:\r<BR>\n" );
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document.write( "x = 18/2 which simplifies to x = 9.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "let's see if it's good.\r<BR>\n" );
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document.write( "the whole trip is 9 kilometers.\r<BR>\n" );
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document.write( "he traveled 1 kilometer plus half of the rest which means he traveled 1 kilometer plus 1/2 * 8 = 1 + 4 = 5 kilometers.\r<BR>\n" );
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document.write( "what remained to be traveled was 1 + 1/3 * the whole trip which means what remained to be traveled = 1 + 1/3 * 9 = 1 + 3 = 4 kilometers.\r<BR>\n" );
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document.write( "he traveled 5 kilometers.<BR>\n" );
document.write( "he had 4 kilometers left to be traveled.\r<BR>\n" );
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document.write( "5 + 4 = 9 which is equal to the whole trip.\r<BR>\n" );
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document.write( "solution looks good.<BR>\n" );
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