document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068792>Question 1068792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John asked Jack how old he is. Jack replied: I am twice as old as you were when I was your age; when you are my age, our ages together will be 63. How old is each of them?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #684073 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=684073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= John's age (in years)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= Jack's age (in years),<BR>\n" );
document.write( "and we assume no tricks, as if both had birthdays on the same day.<BR>\n" );
document.write( "Jack uses the phrase \"when I was your age,\" implying that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3Ex ALIGN=MIDDLE  ALT=\"y%3Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but we know that the difference in ages is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x ALIGN=MIDDLE  ALT=\"y-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > years.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x ALIGN=MIDDLE  ALT=\"y-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > years ago, Jack was Jon's age, and<BR>\n" );
document.write( "John was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x ALIGN=MIDDLE  ALT=\"y-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > years younger than he is now, so his age was<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%28y-x%29=x-y%2Bx=2x-y ALIGN=MIDDLE  ALT=\"x-%28y-x%29=x-y%2Bx=2x-y\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Jack says he is twice as old as that, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%282x-y%29 ALIGN=MIDDLE  ALT=\"y=2%282x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x-2y ALIGN=MIDDLE  ALT=\"y=4x-2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283y=4x%29 ALIGN=MIDDLE  ALT=\"highlight%283y=4x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Jack says \"when you are my age, our ages together will be 63.\"<BR>\n" );
document.write( "That is in the future, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x ALIGN=MIDDLE  ALT=\"y-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > years into the future,<BR>\n" );
document.write( "since that is the difference in their ages.<BR>\n" );
document.write( "At that point,<BR>\n" );
document.write( "John's age will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Jack's current age), and<BR>\n" );
document.write( "Jack's age will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B%28y-x%29=2y-x ALIGN=MIDDLE  ALT=\"y%2B%28y-x%29=2y-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The sum of their ages at that point will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B%282y-x%29=63 ALIGN=MIDDLE  ALT=\"y%2B%282y-x%29=63\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283y-x=63%29 ALIGN=MIDDLE  ALT=\"highlight%283y-x=63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We have a system of 2 linear equations with 2 variables to solve.<BR>\n" );
document.write( "There are many ways to go from initial set of equations to solutions.<BR>\n" );
document.write( "Here is the scenic zig-zaggy way:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283y=4x%2C3y-x=63%29 ALIGN=MIDDLE  ALT=\"system%283y=4x%2C3y-x=63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283y=4x%2C4x-x=63%29 ALIGN=MIDDLE  ALT=\"system%283y=4x%2C4x-x=63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283y=4x%2C3x=63%29 ALIGN=MIDDLE  ALT=\"system%283y=4x%2C3x=63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=4x%2F3%2C3x=63%29 ALIGN=MIDDLE  ALT=\"system%28y=4x%2F3%2C3x=63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=4x%2F3%2Cx=63%2F3%29 ALIGN=MIDDLE  ALT=\"system%28y=4x%2F3%2Cx=63%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=4x%2F3%2Cx=21%29 ALIGN=MIDDLE  ALT=\"system%28y=4x%2F3%2Cx=21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=4%2A21%2F3%2Cx=21%29 ALIGN=MIDDLE  ALT=\"system%28y=4%2A21%2F3%2Cx=21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28y=28%2Cx=21%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28y=28%2Cx=21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );