document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=282360>Question 282360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is the problem and they want an algebra solution.<BR>\n" );
document.write( "Three tired and hungry men went to sleep with a bag of apples. One man woke up, ate 1/3 of the apples, then went back to sleep. Later a second man woke up and ate 1/3 of the remaining apples, then went back to sleep.Finally,the third man woke and ate 1/3 of the remaining apples. When he was finished there were 8 apples left. 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 #205045 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=205045\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the number of apples there were originally.\r<BR>\n" );
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document.write( "First man eats 1/3 * x, so you are left with 2/3 * x\r<BR>\n" );
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document.write( "Second man eats 1/3 * 2/3 * x which equals 2/9 * x.\r<BR>\n" );
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document.write( "2/3 * x - 2/9 * x equals 6/9 * x - 2/9 * x equsls 4/9 * x\r<BR>\n" );
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document.write( "Third man eats 1/3 * 4/9 * x which equals 4/27 * x.\r<BR>\n" );
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document.write( "4/9 * x - 4/27 * x equals 12/9 * x - 4/27 * x equals 8/27 * x\r<BR>\n" );
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document.write( "After everybody gets their fill, you are left with 8/27 * x\r<BR>\n" );
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document.write( "Since there are 8 apples left, this means that 8/27 * x = 8\r<BR>\n" );
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document.write( "Multiply both sides of this equation by 27 to get:\r<BR>\n" );
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document.write( "8 * x = 27 * 8\r<BR>\n" );
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document.write( "Divide both sides of this equation by 8 to get:\r<BR>\n" );
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document.write( "x = 27\r<BR>\n" );
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document.write( "The original number of apples is 27.\r<BR>\n" );
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document.write( "To prove, substitute 27 for x and go through the original problem again.\r<BR>\n" );
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document.write( "There are 27 apples.\r<BR>\n" );
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document.write( "First man eats 1/3 * 27 = 9.\r<BR>\n" );
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document.write( "27 - 9 = 18\r<BR>\n" );
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document.write( "Second man eats 1/3 * 18 = 6.\r<BR>\n" );
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document.write( "18 - 6 = 12.\r<BR>\n" );
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document.write( "Third man eats 1/3 * 12 = 4.\r<BR>\n" );
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document.write( "12 - 4 = 8\r<BR>\n" );
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document.write( "There are 8 apples left when the original number is 27.\r<BR>\n" );
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document.write( "That's your answer.\r<BR>\n" );
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document.write( "I also looked at it again and solved it this way:\r<BR>\n" );
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document.write( "x - (1/3)x = (2/3)x = a<BR>\n" );
document.write( "a - (1/3)a = (2/3)a = b<BR>\n" );
document.write( "b - (1/3)b = (2/3)b = c\r<BR>\n" );
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document.write( "I got:\r<BR>\n" );
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document.write( "(2/3)x = a<BR>\n" );
document.write( "(2/3)a = b<BR>\n" );
document.write( "(2/3)b = c\r<BR>\n" );
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document.write( "Working back from (2/3)b = c, I then substituted (2/3)a for b and got:\r<BR>\n" );
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document.write( "(2/3)*(2/3)*a = c\r<BR>\n" );
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document.write( "I then substituted x for a to get:\r<BR>\n" );
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document.write( "(2/3)*((2/3)*2/3)*x = c\r<BR>\n" );
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document.write( "I simplified this to get:\r<BR>\n" );
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document.write( "(8/27)x = c\r<BR>\n" );
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document.write( "Since c = 8 which was the number of apples left after everybody had their fill, I got:\r<BR>\n" );
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document.write( "(8/27)x = 8\r<BR>\n" );
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document.write( "I multiplied both sides of this equation by 27 to get:\r<BR>\n" );
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document.write( "8x = 8*27\r<BR>\n" );
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document.write( "I divided both sides of this equation by 8 to get:\r<BR>\n" );
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document.write( "x = 27.\r<BR>\n" );
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document.write( "That's your answer again looking at it a slightly different way.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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