document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464882>Question 464882</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the ages of a married couple and their four children is 40 years over the century mark. Ten years ago, the sum f the ages of the couple, the eldest child and the second cild is 5 decades and 5 years less than the sum of all (the six of them) their ages now. The fatherīs age is 10 times the age of the youngest, while the motherīs age is 8 times that of the youngest. The difference between the age of the second cild and the sum of the ages of the third and the last child is zero, while the difference between the ages of the first child and the sum of the ages of the second and last child is also zero. How old is the father now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318470 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f\"> represent the father's age.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> represent the mothers age, and let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_1,\ \ \"><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_2,\ \ \"><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_3,\ \ \">and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_4\"> represent the ages of child 1, 2, 3, and 4.\r<BR>\n" );
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document.write( "The first thing we know is that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f\ +\ m\ +\ c_1\ +\ c_2\ +\ c_3\ +\ c_4\ =\ 140\"> (Eq 1)\r<BR>\n" );
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document.write( "The next thing we are told is something about the situation 10 years ago:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f\ -\ 10\ +\ m\ -\ 10\ +\ c_1\ -\ 10\ +\ c_2\ -\ 10\ =\ 140\ -\ 55\">\r<BR>\n" );
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document.write( "Which can be simplified to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f\ +\ m\ +\ c_1\ +\ c_2\ =\ 125\"> (Eq 2)\r<BR>\n" );
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document.write( "Then we are told that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f\ =\ 10c_4\"> (Eq 3)\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ 8c_4\"> (Eq 4)\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c_2\ -\ (c_3\ +\ c_4)\ =\ 0\"> (Eq 5)\r<BR>\n" );
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document.write( "and finally:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c_1\ -\ (c_2\ +\ c_4)\ =\ 0\">  (Eq 6)\r<BR>\n" );
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document.write( "Notice the handy (and very necessary) fact that we have 6 equations to match our 6 variables.\r<BR>\n" );
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document.write( "Start by combining Equations 1 and 2.  Multiply (2) by -1 and add the result to (1) with the following result:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c_3\ +\ c_4\ =\ 15\"> (Eq 7)\r<BR>\n" );
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document.write( "Which can be written as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c_3\ =\ 15\ -\ c_4\"> (Eq 8)\r<BR>\n" );
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document.write( "Substituting the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_3\ +\ c_4\"> from Equation 7 into Equation 5, we can deduce that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c_2\ =\ 15\"> (Eq 9)\r<BR>\n" );
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document.write( "Using the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_2\"> from Equation 9 in Equation 6, we can deduce that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ c_1\ =\ c_4\ +\ 15\"> (Eq 10)\r<BR>\n" );
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document.write( "Notice that we now have an expression for each of the variables <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f,\ \ \"><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m,\ \ \"><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_1,\ \ \"><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_2,\ \ \">and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_3\"> in terms of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_4\">, (Equations 3, 4, 10, 9, and 8) so make all of the appropriate substitutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10c_4\ +\ 8c_4\ +\ c_4\ +\ 15\ +\ 15\ +\ 15\ -\ c_4\ +\ c_4\ =\ 140\">\r<BR>\n" );
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document.write( "The rest is simply solving the single variable equation for the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c_4\"> to get the youngest child's age and then multiplying by 10 to get the father's age.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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