document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170205>Question 170205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thanks so much for all the help!!! I have one last one that I think I have some clue about but not sure:\r<BR>\n" );
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document.write( "A man is carrying rice on a journey. He passes through three custom stations. At the first he gives up 1/3 of his rice; at the second he is allowed to keep 1/3 of what is left; at the third he gives up 1/4 of what remains. After passing through all three custom stations, he has 6 pounds less than he started with. How much rice did he have when he started? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125643 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=125643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=amount of rice he starts with and y=amount he has leftover\r<BR>\n" );
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document.write( "<h4>After First Station</h4>\r<BR>\n" );
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document.write( "Since \"At the first he gives up 1/3 of his rice\", this tells us that after the first station, he has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%281%2F3%29x ALIGN=MIDDLE  ALT=\"x-%281%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > pounds of rice leftover\r<BR>\n" );
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document.write( "Note: I've subtracted 1/3 of the amount \"x\" from \"x\"\r<BR>\n" );
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document.write( "Combine like terms to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x ALIGN=MIDDLE  ALT=\"%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So he has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x ALIGN=MIDDLE  ALT=\"%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > pounds of rice leftover after the first station (this makes sense because the guard took 1/3 so the man must have 2/3 leftover).\r<BR>\n" );
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document.write( "Note: remember, the \"x\" is just a number (a number in which we do NOT know). However, to help you get an idea of what is going on, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12 ALIGN=MIDDLE  ALT=\"x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie let's say that he started at 12 lbs of rice). After the first station, he would have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%2912=24%2F3=8 ALIGN=MIDDLE  ALT=\"%282%2F3%2912=24%2F3=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > lbs of rice.\r<BR>\n" );
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document.write( "<h4>After Second Station</h4>\r<BR>\n" );
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document.write( "Keep in mind that the man still has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x ALIGN=MIDDLE  ALT=\"%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > lbs of rice. \r<BR>\n" );
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document.write( "Since at \"the second he is allowed to keep 1/3 of what is left\", this means that they will take 2/3 of what he has left. \r<BR>\n" );
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document.write( "So this means that you need to subtract like this\r<BR>\n" );
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document.write( "Amount he has left - (2/3)*(Amount he has left )\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x+-+%282%2F3%29%2A%28%282%2F3%29x%29 ALIGN=MIDDLE  ALT=\"%282%2F3%29x+-+%282%2F3%29%2A%28%282%2F3%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x+-+%284%2F9%29x ALIGN=MIDDLE  ALT=\"%282%2F3%29x+-+%284%2F9%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F9%29x ALIGN=MIDDLE  ALT=\"%282%2F9%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
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document.write( "So after the second station, he has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F9%29x ALIGN=MIDDLE  ALT=\"%282%2F9%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > lbs of rice left.\r<BR>\n" );
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document.write( "<h4>After Third Station</h4>\r<BR>\n" );
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document.write( "Finally, because \"at the third he gives up 1/4 of what remains\", this tells us that we subtract 1/4 of what he has left like this:\r<BR>\n" );
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document.write( "Amount he has left - (1/4)*(Amount he has left )\r<BR>\n" );
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document.write( "Which algebraically looks like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F9%29x-%281%2F18%29x ALIGN=MIDDLE  ALT=\"%282%2F9%29x-%281%2F18%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29x ALIGN=MIDDLE  ALT=\"%281%2F6%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
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document.write( "So after the third station, he has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29x ALIGN=MIDDLE  ALT=\"%281%2F6%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > lbs of rice left.\r<BR>\n" );
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document.write( "Since \"he has 6 pounds less than he started with.\" this means that he ended up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-6 ALIGN=MIDDLE  ALT=\"x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > lbs. Also, we know that he ended up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29x ALIGN=MIDDLE  ALT=\"%281%2F6%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > lbs of rice (after passing through the third station)\r<BR>\n" );
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document.write( "So this means that the two are equal, so...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-36=x ALIGN=MIDDLE  ALT=\"6x-36=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD 6 to clear the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=x%2B36 ALIGN=MIDDLE  ALT=\"6x=x%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-x=36 ALIGN=MIDDLE  ALT=\"6x-x=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=36 ALIGN=MIDDLE  ALT=\"5x=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2836%29%2F%285%29 ALIGN=MIDDLE  ALT=\"x=%2836%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the man started with 7.2 lbs of rice and the amounts after each station are:\r<BR>\n" );
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document.write( "1st station: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%287.2%29=4.8 ALIGN=MIDDLE  ALT=\"%282%2F3%29%287.2%29=4.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > so he had 4.8 lbs after the 1st station\r<BR>\n" );
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document.write( "2nd station: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F9%29%287.2%29=1.6 ALIGN=MIDDLE  ALT=\"%282%2F9%29%287.2%29=1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > so he had 1.6 lbs after the 2nd station\r<BR>\n" );
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document.write( "3rd station: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29%287.2%29=1.2 ALIGN=MIDDLE  ALT=\"%281%2F6%29%287.2%29=1.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so he had 1.2 lbs after the 3rd station\r<BR>\n" );
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document.write( "Since the difference between 7.2 and 1.2 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.2-1.2=6 ALIGN=MIDDLE  ALT=\"7.2-1.2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > this helps confirm our answer.\r<BR>\n" );
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