document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183664>Question 1183664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bill is 5 times older than Keira, Bill is 5 times older than Phil, Oscar is twice as old as Bill, <BR>\n" );
document.write( "and the total age of all of them at 81. How old is Phil? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814083 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=814083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "ANSWER: NO SOLUTION!<br><BR>\n" );
document.write( "The statement of the problem is faulty.  Age problems need to have answers that are whole numbers; this one does not -- regardless of how it is interpreted.<br><BR>\n" );
document.write( "The statement of a math problem should never say that one person is \"5 times OLDER THAN\" another person.<br><BR>\n" );
document.write( "In sloppy everyday English usage, \"5 times OLDER THAN\" and \"5 times AS OLD AS\" are used to mean the same thing, but they do not.  If the first person's age is x, then the age of a person 5 times AS OLD AS the first is clearly 5 times x, or 5x.  But if the age of the second person is 5 times OLDER THAN the first, then that person's age is x, PLUS 5 MORE TIMES x, which is x+5x=6x.<br><BR>\n" );
document.write( "This problem is faulty in that the answers are not whole numbers with either interpretation of the given information.<br><BR>\n" );
document.write( "(1) If we incorrectly use 5 times older than x to mean 5x, then<BR>\n" );
document.write( "Phil = x<BR>\n" );
document.write( "Bill = 5x<BR>\n" );
document.write( "Keira = x<BR>\n" );
document.write( "Oscar = 10x<br><BR>\n" );
document.write( "The sum of their ages is 81:<BR>\n" );
document.write( "17x=81<BR>\n" );
document.write( "x = 81/17 not a whole number<br><BR>\n" );
document.write( "(2) if we correctly use 5 times older than x to mean 6x, then<BR>\n" );
document.write( "Phil = x<BR>\n" );
document.write( "Bill = 6x<BR>\n" );
document.write( "Keira = x<BR>\n" );
document.write( "Oscar = 12x<br><BR>\n" );
document.write( "20x=81<BR>\n" );
document.write( "x = 81/20 not a whole number<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );