document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=513481>Question 513481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> robert is one half as old as his father. twele years ago, robert was one-third as old as his father was then. find their present ages. steps would help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #343016 by </B><A HREF=/tutors/aboutme.mpl?userid=drcole><B>drcole(72)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drcole><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=343016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x represent Robert's age right now.  Let y represent Robert's father's age right now.  We know that Robert is one half as old as his father, and we can represent this fact in an equation as:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%281%2F2%29+%2A+y+ ALIGN=MIDDLE  ALT=\"+x+=+%281%2F2%29+%2A+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+=+y+ ALIGN=MIDDLE  ALT=\"+2x+=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (multiplying both sides by 2)\r<BR>\n" );
document.write( "\n" );
document.write( "For our second fact, we need to consider Robert's age and his father's age twelve years ago.  If Robert is x years old right now, he was x - 12 years old twelve years ago.  Similarly, Robert's father was y - 12 years old twelve years ago.  We are told that, twelve years ago, Robert was one third the age of his father.  As an equation, we can represent this fact as:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+-+12%29+=+%281%2F3%29+%2A+%28y+-+12%29+ ALIGN=MIDDLE  ALT=\"+%28x+-+12%29+=+%281%2F3%29+%2A+%28y+-+12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2A%28x+-+12%29+=+y+-+12+ ALIGN=MIDDLE  ALT=\"+3%2A%28x+-+12%29+=+y+-+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (multiplying both sides by 3)\r<BR>\n" );
document.write( "\n" );
document.write( "Now we combine our two facts to find x (and then, y): from our first fact, we know that 2x = y.  So we substitute 2x in for y in the second equation, and solve for x:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2A%28x+-+12%29+=+2x+-+12+ ALIGN=MIDDLE  ALT=\"+3%2A%28x+-+12%29+=+2x+-+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (substituting 2x for y)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+36+=+2x+-+12+ ALIGN=MIDDLE  ALT=\"+3x+-+36+=+2x+-+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (distributing 3 on the left hand side)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+36+=+-12+ ALIGN=MIDDLE  ALT=\"+x+-+36+=+-12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (subtracting 2x from both sides)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+24+ ALIGN=MIDDLE  ALT=\"+x+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (adding 36 to both sides)\r<BR>\n" );
document.write( "\n" );
document.write( "Thus x = 24, meaning Robert is currently 24 years old.  Since y = 2x, Robert's father is currently twice his age, or 48 years old.  To check, note that twelve years ago, Robert was 12 years old and Robert's father was 36 years old, or three times his age back then, so these numbers fit both facts. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );