document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200200>Question 1200200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bottle filled with varnish cost $1.10. if the varnish alone is worth $1.00 more than the bottle, find the value of the bottle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834270 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</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=834270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A bottle filled with varnish cost $1.10. if the varnish alone is worth $1.00 more <BR>\n" );
document.write( "than the bottle, find the value of the bottle.<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem and many other similar problems is/are well known &nbsp;\" trap \" &nbsp;problem/problems.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Those, who do not know that it is a trap, &nbsp;usually fall in it,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;especially those of them who are in hurry to answer without thinking &nbsp;(and without checking).\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The answer &nbsp;$1.00 &nbsp;and &nbsp;$0.10, &nbsp;given by the other person, &nbsp;is, &nbsp;OBVIOUSLY, &nbsp;incorrect\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(because the difference of &nbsp;$1.00 &nbsp;and &nbsp;$0.10 &nbsp;is not &nbsp;$1.00).\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The correct answer is &nbsp;$0.05 &nbsp;for the empty bottle and &nbsp;$1.05 &nbsp;for the varnish alone.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;One way to get the correct answer is to get it mentally, &nbsp;after thinking couple of seconds.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Another way is to solve it formally, &nbsp;as follows.\r<BR>\n" );
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document.write( "x   dollars for varnish;\r\n" );
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document.write( "x-1 dollars for the bottle.\r\n" );
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document.write( "Total cost equation\r\n" );
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document.write( "    x + (x-1) = 1.10  dollars\r\n" );
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document.write( "    x + x = 1.10 + 1\r\n" );
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document.write( "     2x   =   2.10\r\n" );
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document.write( "      x   =   2.10/2 = 1.05,\r\n" );
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document.write( "giving the above mentioned correct answer.\r\n" );
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document.write( "Solved, with complete explanations.\r<BR>\n" );
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document.write( "You may ask me, regarding this and other similar trap problems - - - how to avoid falling in such trap, \r<BR>\n" );
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document.write( "if you do not know about it in advance ?  &nbsp;&nbsp;Is there a way ?  &nbsp;&nbsp;Does it exist ?\r<BR>\n" );
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document.write( "The answer is: &nbsp;&nbsp;YES, &nbsp;the way does exist.\r<BR>\n" );
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document.write( "This way is to &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28CHECK%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28CHECK%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;&nbsp;your answer before you release it to outside.\r<BR>\n" );
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document.write( "By the way, &nbsp;checking is absolutely necessary step of each problem solution.\r<BR>\n" );
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document.write( "Without it, &nbsp;no one answer can be accepted.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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