document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980579>Question 980579</A>: <I><SPAN STYLE=\"word-break: break-all;\">     -Adrian and Betty have been teaching for a total of 36 years.\r<BR>\n" );
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document.write( "            -Charlie and Betty have been teaching for a total of 22 years.\r<BR>\n" );
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document.write( "            -Charlie and Adrian have been teaching for a total of 28 years.\r<BR>\n" );
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document.write( "How long has each been teaching? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601724 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53763)</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=601724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Let &nbsp;<B>a</B>&nbsp; be the number of years Adrian has been teaching.\r<BR>\n" );
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document.write( "Let &nbsp;<B>b</B>&nbsp; be the number of years Betty has been teaching.\r<BR>\n" );
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document.write( "Let &nbsp;<B>c</B>&nbsp; be the number of years Charlie has been teaching.\r<BR>\n" );
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document.write( "Then we have the system of three equations in three unknowns\r<BR>\n" );
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document.write( "a + b &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 36, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1)\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;b + c = 22, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)\r<BR>\n" );
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document.write( "a + &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c = 28. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(3)\r<BR>\n" );
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document.write( "It is very special kind of system, &nbsp;and we will apply special method to solve it.\r<BR>\n" );
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document.write( "Add all three equations &nbsp;(left sides and right sides separately).\r<BR>\n" );
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document.write( "You will get \r<BR>\n" );
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document.write( "2(a + b + c) = 86, &nbsp;&nbsp;&nbsp;&nbsp;or\r<BR>\n" );
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document.write( "a + b + c = 43. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(4)\r<BR>\n" );
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document.write( "Now, &nbsp;distract the equation &nbsp;(1)&nbsp; from the equation &nbsp;(4). &nbsp;You will get \r<BR>\n" );
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document.write( "c = 43 - 36 = 7.\r<BR>\n" );
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document.write( "Hence, &nbsp;Charlie has been teaching for &nbsp;7&nbsp; years.\r<BR>\n" );
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document.write( "Next, &nbsp;distract the equation &nbsp;(2)&nbsp; from the equation &nbsp;(4). &nbsp;You will get \r<BR>\n" );
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document.write( "a = 43 - 22 = 21.\r<BR>\n" );
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document.write( "Hence, &nbsp;Adrian has been teaching for &nbsp;21&nbsp; years.\r<BR>\n" );
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document.write( "Next, &nbsp;distract the equation &nbsp;(3)&nbsp; from the equation &nbsp;(4). &nbsp;You will get \r<BR>\n" );
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document.write( "b = 43 - 28 = 15.\r<BR>\n" );
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document.write( "Hence, &nbsp;Betty has been teaching for &nbsp;15&nbsp; years.\r<BR>\n" );
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document.write( "For more problems similar to this one see the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/The-trick-to-solve-some-word-problems-with-three-and-more-unknowns.lesson>The tricks to solve some word problems with three and more unknowns using mental math</A>&nbsp; in this site. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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