document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208344>Question 1208344</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Alan Ben and Caleb shared some marbles. Alan took 40% of the marbles and was given 1 more . Ben took 25% of the remaining and was given 3 more. Caleb took the remaining 12 marbles. How many were there at first. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846707 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846707\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Alan Ben and Caleb shared some marbles. Alan took 40% of the marbles and was given 1 more . <BR>\n" );
document.write( "Ben took 25% of the remaining and was given 3 more. <BR>\n" );
document.write( "Caleb took the remaining 12 marbles. How many were there at first.<BR>\n" );
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document.write( "Let T be the total number of marbles.\r\n" );
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document.write( "Alan has 0.4T +1 marbles;  the remaining is T - (0.4T+1) = 0.6T-1.\r\n" );
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document.write( "Ben has 0.25(0.6T-1) + 3 marbles;\r\n" );
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document.write( "Caleb has 12 marbles.\r\n" );
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document.write( "Write an equation for the total\r\n" );
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document.write( "    (0.4T + 1) + (0.25(0.6T-1) + 3) + 12 = T.\r\n" );
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document.write( "Simplify and find T\r\n" );
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document.write( "    0.4T + 1 + 0.15T - 0.25 + 3 + 12 = T\r\n" );
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document.write( "    0.55T + 15.75 = T\r\n" );
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document.write( "    15.75 = T - 0.55T\r\n" );
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document.write( "    15.75 = 0.45T\r\n" );
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document.write( "     T = 15.75/0.45 = 35.\r\n" );
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document.write( "<U>ANSWER</U>.  The total number of marbles is/was 35.\r\n" );
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document.write( "          This total number of marbles was not changed before and after: it remained THE SAME.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "The question in the problem is posed INCORRECTLY.\r<BR>\n" );
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document.write( "The correct question is: \"How many marbles were there in total ?\"\r<BR>\n" );
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document.write( "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\r<BR>\n" );
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document.write( "Let me explain you, WHY I think that the question is posed incorrectly<BR>\n" );
document.write( "and WHY a TRUE question should be posed differently.\r<BR>\n" );
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document.write( "In this problem, the marbles were distributed inside some group of three people.<BR>\n" );
document.write( "No marbles went outside. Therefore, the total number of marbles at the beginning was  <BR>\n" );
document.write( "the same as at the end.  So, there is a hidden symmetry between the future and the past<BR>\n" );
document.write( "in this problem. The symmetry is that the number of the marbles at the origin<BR>\n" );
document.write( "and at the end is the same.\r<BR>\n" );
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document.write( "If the problem's creator  formulates the problem according to my instruction, he (or she) <BR>\n" );
document.write( "demonstrates that he/she recognizes this symmetry and does not violate it.  <BR>\n" );
document.write( "If he/she formulates differently, he/she demonstrates that he/she does not care <BR>\n" );
document.write( "about his/her language and leaves to the reader to figure out these details on his/her own. <BR>\n" );
document.write( "My point is that the problem should sound harmonically, should be posed clearly <BR>\n" );
document.write( "and should not distract the reader from the essence of the task.\r<BR>\n" );
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document.write( "That's all. \r<BR>\n" );
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document.write( "Behind all this is respect / (or disrespect) for the symmetry, for the harmony and for the reader.\r<BR>\n" );
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document.write( "Nothing more and nothing else.\r<BR>\n" );
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