document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237340>Question 237340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me understand how to solve the following problem? \r<BR>\n" );
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document.write( "Three tired and hungry people had a big bag of apples. While the other two were asleep, one of the three awoke, ate one-third of the apples, and went back to sleep. Later a second person awoke, ate one-third of the remaining apples and went back to sleep. Finally, the third person awoke and ate one-third of the remaining apples, leaving 8 apples in the bag. How many apples were in the bag originally?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174541 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = original number of apples in the bag \r<BR>\n" );
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document.write( "x-1/3x= 2/3x = number of apples left after the first person \r<BR>\n" );
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document.write( "The second person ate 1/3 of those that were left, so <BR>\n" );
document.write( "1/3*2/3x= 2/9x apples = number of apples eaten by the second person.\r<BR>\n" );
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document.write( "This leaves (2/3)x-(2/9)x which is (6/9)x - (2/9)x or 4/9x apples left after the second person.\r<BR>\n" );
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document.write( "The third person ate 1/3 of the 4/9x apples, which is 4/27x apples.\r<BR>\n" );
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document.write( "This leaves (4/9)x-(4/27)x apples after the third person, which is <BR>\n" );
document.write( "(12/27)x-(4/27)x or (8/27)x.\r<BR>\n" );
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document.write( "So the equation is, based upon the number of apples left being equal to 8: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F27%29x=8 ALIGN=MIDDLE  ALT=\"%288%2F27%29x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply both sides of the equation by the reciprocal of (8/27) which is (27/8), and you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2827%2F8%29%2A%288%2F27%29x=+%2827%2F8%29%2A8 ALIGN=MIDDLE  ALT=\"%2827%2F8%29%2A%288%2F27%29x=+%2827%2F8%29%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x= 27 apples.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "The first person eats 1/3 of 27 which is 9 apples, leaving 18 apples.\r<BR>\n" );
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document.write( "The second person eats 1/3 of 18 which is 6 apples, leaving 12.\r<BR>\n" );
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document.write( "The third person eats 1/3 of 12 which is 4 apples, leaving 8 apples.\r<BR>\n" );
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document.write( "VERY NICE PROBLEM!!!\r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje, Retired<BR>\n" );
document.write( "Seminole State College of Florida<BR>\n" );
document.write( "Altamonte Springs Campus </SPAN>\n" );
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