document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191544>Question 1191544</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John is X years old<BR>\n" );
document.write( "Jill is 2 years younger than John<BR>\n" );
document.write( "Tom (John's dad) is 2x older than John plus 8 years\r<BR>\n" );
document.write( "\n" );
document.write( "How old is John, Jill and Tom<BR>\n" );
document.write( "Total ages added together is 82<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823348 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823348\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Technically, the problem as stated has no solution in whole numbers and is therefore invalid.<br><BR>\n" );
document.write( "The problem is that a phrase like \"2 times older than\" should NEVER be used in the statement of a problem, because its meaning is NOT what most people think it is.<br><BR>\n" );
document.write( "Given an age n, the age \"2 times AS OLD AS\" n is clearly 2*n = 2n.  That is clearly what the intent of this problem is.<br><BR>\n" );
document.write( "But if an age n is given, and another age is \"2 times OLDER THAN\" n, then the grammatically correct interpretation is that the other age is n, PLUS 2 TIMES MORE n, which is n+2n=3n.<br><BR>\n" );
document.write( "(Note that corresponds to saying that a number INCREASED BY 200%, becomes 100%+200% = 300% of the original number.)<br><BR>\n" );
document.write( "So \"2 times older than\" means \"3 times as old as\".<br><BR>\n" );
document.write( "Then the correct interpretation of the problem as written is<BR>\n" );
document.write( "x = John's age<BR>\n" );
document.write( "x-2 = Jill's age<BR>\n" );
document.write( "3x+8 = Tom's age<br><BR>\n" );
document.write( "And the equation that says the sum of their ages is 82 leads to non-integer values:<br><BR>\n" );
document.write( "x+(x-2)+(3x+8)=82<BR>\n" );
document.write( "5x+6=82<BR>\n" );
document.write( "5x=76<BR>\n" );
document.write( "x=15.2<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );