document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188483>Question 188483</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lea is 6 years older than Phil. John is 5 years older than Lea. How old is Sue if the total age of everyone equals 41? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141312 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=141312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "I think you left out a small piece of information because with the information given you can only create 1 equation in 2 variables.  However, if we constrain the value of the variables to the positive integers, you can develop either 7 or 9 solutions depending on whether or not you consider 0 (as in a newborn infant) to be a valid \"age\" in the sense of this question.\r<BR>\n" );
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document.write( "Let <i>x</i> be John's age.\r<BR>\n" );
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document.write( "Then <i>x</i> - 5 is Lea's age and <i>x</i> - 5 - 6 = <i>x</i> - 11 is Phil's age.\r<BR>\n" );
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document.write( "Sue's age, given that there are no other clues, is <i>y</i>\r<BR>\n" );
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document.write( "And the sum is 41, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x + (x - 5) + (x - 11) + y = 41\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x - 16 + y = 41\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x = 57 - y\">\r<BR>\n" );
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document.write( "In order for <i>x</i> to be a positive integer, 57 - <i>y</i> must be evenly divisible by 3.  In order for <i>x</i> - 11 to be a positive integer, <i>x</i> must be greater than or equal to 11.  Hence, and the demonstration is left as an exercise for the student, the possibilities are:\r<BR>\n" );
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document.write( "Sue:  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{y\ |\ y\ \in\ \I,\ 0\ \leq\ y\ \leq\ 23,\ \text{mod}(y,\,3)\,=\,0\}\">\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 \ \ \ \ \ \ \ \ \ \ \{x\ |\ x\ \in\ \I,\ 11\ \leq\ x\ \leq\ 19\}\">\r<BR>\n" );
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document.write( "Lea:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x - 5\">\r<BR>\n" );
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document.write( "Phil:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x - 11\">\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" );
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