document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978179>Question 978179</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My age this year is a multiple of 8.Next year it will be a multiple of 7.How old am i? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599646 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=599646\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> TRIAL AND ERROR:<BR>\n" );
document.write( "the current age is a multiple of 8, so we try different multiples of 8.<BR>\n" );
document.write( "We can make a table with reasonable ages that are multiples of 8,<BR>\n" );
document.write( "and see if the age next year (age+1) would be a multiple of 7.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C14%2Cage%2C8%2C16%2C24%2C32%2C40%2C48%2C56%2C64%2C72%2C80%2C88%2C96%2C104%2Cage%2B1%2C9%2C17%2C25%2C32%2C41%2C49%2C57%2C65%2C73%2C81%2C89%2C97%2C105%2C%227+X+__+%3F%22%2CNO%2C+NO%2C+NO%2C+NO%2CNO%2C%22YES%21%22%2CNO%2CNO%2C+NO%2C+NO%2C+NO%2C+NO%2C%22%3F%3F%3F%21%21%21%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The age of that person should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2848%29 ALIGN=MIDDLE  ALT=\"highlight%2848%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > this year, and will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49 ALIGN=MIDDLE  ALT=\"49\"   DISABLED_style= \"max-width:90%; height:auto;\" > at some time next year.<BR>\n" );
document.write( "A person could be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=104 ALIGN=MIDDLE  ALT=\"104\"   DISABLED_style= \"max-width:90%; height:auto;\" > and expect to have another birthday next year,<BR>\n" );
document.write( "but it is very rare to be that old,<BR>\n" );
document.write( "and someone that old would probably not be asking math question like that one.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "MAKING IT LOOK MORE LIKE ALGEBRA:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8n ALIGN=MIDDLE  ALT=\"8n\"   DISABLED_style= \"max-width:90%; height:auto;\" >= age this year (for some number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > that is a positive integer).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8n%2B1=7p ALIGN=MIDDLE  ALT=\"8n%2B1=7p\"   DISABLED_style= \"max-width:90%; height:auto;\" >= age next year (for some number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > that is a positive integer).<BR>\n" );
document.write( "Let us get some useful relationship from that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8n%2B1=7p ALIGN=MIDDLE  ALT=\"8n%2B1=7p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7n%2Bn%2B1=7p ALIGN=MIDDLE  ALT=\"7n%2Bn%2B1=7p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1=7p-7n ALIGN=MIDDLE  ALT=\"n%2B1=7p-7n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1=7%28p-n%29 ALIGN=MIDDLE  ALT=\"n%2B1=7%28p-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a positive integer, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p-n ALIGN=MIDDLE  ALT=\"p-n\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be a positive integer too.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p-n=1 ALIGN=MIDDLE  ALT=\"p-n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1=7 ALIGN=MIDDLE  ALT=\"n%2B1=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=7-1 ALIGN=MIDDLE  ALT=\"n=7-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=6 ALIGN=MIDDLE  ALT=\"n=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=age=8n ALIGN=MIDDLE  ALT=\"age=8n\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28age=8n%2Cn=6%29 ALIGN=MIDDLE  ALT=\"system%28age=8n%2Cn=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28age=8n%2C8n=8%2A6%29 ALIGN=MIDDLE  ALT=\"system%28age=8n%2C8n=8%2A6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28age=48%29 ALIGN=MIDDLE  ALT=\"highlight%28age=48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p-n%3E=2 ALIGN=MIDDLE  ALT=\"p-n%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1%3E=14 ALIGN=MIDDLE  ALT=\"n%2B1%3E=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3E=14-1 ALIGN=MIDDLE  ALT=\"n%3E=14-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3E=13 ALIGN=MIDDLE  ALT=\"n%3E=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=age=8n ALIGN=MIDDLE  ALT=\"age=8n\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28age=8n%2Cn%3E=13%29 ALIGN=MIDDLE  ALT=\"system%28age=8n%2Cn%3E=13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28age=8n%2C8n%3E=8%2A13%29 ALIGN=MIDDLE  ALT=\"system%28age=8n%2C8n%3E=8%2A13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=age%3E=104 ALIGN=MIDDLE  ALT=\"age%3E=104\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which not a very reasonable answer, as it is unlikely to reach age 104<BR>\n" );
document.write( "while expecting to live until the next year and the next birthday,<BR>\n" );
document.write( "and asking this kind of math question.<BR>\n" );
document.write( "However, if I am in good physical and mental health 40 years from now,<BR>\n" );
document.write( "I will post the same question and cackle with glee.\r<BR>\n" );
document.write( "\n" );
document.write( "FOR A TRICK QUESTION<BR>\n" );
document.write( "I do not think it is meant to be a trick question, so I would answer the answer above.<BR>\n" );
document.write( "For a trick question,<BR>\n" );
document.write( "that person could have had a birthday and turned <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56 ALIGN=MIDDLE  ALT=\"56\"   DISABLED_style= \"max-width:90%; height:auto;\" > earlier this yea.<BR>\n" );
document.write( "So, at the beginning of next year would still be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56 ALIGN=MIDDLE  ALT=\"56\"   DISABLED_style= \"max-width:90%; height:auto;\" > (until the next birthday.<BR>\n" );
document.write( "As <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56=8%2A7 ALIGN=MIDDLE  ALT=\"56=8%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "that person's age would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56 ALIGN=MIDDLE  ALT=\"56\"   DISABLED_style= \"max-width:90%; height:auto;\" >= a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > now,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56 ALIGN=MIDDLE  ALT=\"56\"   DISABLED_style= \"max-width:90%; height:auto;\" >= a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some time next year,<BR>\n" );
document.write( "at the beginning of the year, before the next birthday, </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );