document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105932>Question 105932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Robert is 1/2 as old as his father. Twelve years ago he was 1/3 as old as his father was then. Find their present ages </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77083 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=77083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start by letting R = Robert's present age and F = Father's present age.<BR>\n" );
document.write( "From the problem you can write:<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+%281%2F2%29F ALIGN=MIDDLE  ALT=\"R+=+%281%2F2%29F\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"Robert (R) is half as old as his father (F)\"<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R-12+=+%281%2F3%29%28F-12%29 ALIGN=MIDDLE  ALT=\"R-12+=+%281%2F3%29%28F-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"Twelve years ago, he was 1/3 as old as his father was then\"<BR>\n" );
document.write( "So now you have a system of equations with two unknowns (R and F) and you can use any of the accepted methods for solving these for R and F.<BR>\n" );
document.write( "You can simplify these equations by clearing the fractions.<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+%281%2F2%29F ALIGN=MIDDLE  ALT=\"R+=+%281%2F2%29F\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply through by 2.<BR>\n" );
document.write( "1a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2R+=+F ALIGN=MIDDLE  ALT=\"2R+=+F\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R-12+=+%281%2F3%29%28F-12%29 ALIGN=MIDDLE  ALT=\"R-12+=+%281%2F3%29%28F-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply through by 3.<BR>\n" );
document.write( "2a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3R-36+=+F-12 ALIGN=MIDDLE  ALT=\"3R-36+=+F-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now substitute the F from the simplified equation 1a) into the simplified equation 2a).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3R-36+=+2R-12 ALIGN=MIDDLE  ALT=\"3R-36+=+2R-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for R by subtracting 2R from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R-36+=+-12 ALIGN=MIDDLE  ALT=\"R-36+=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 36 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+24 ALIGN=MIDDLE  ALT=\"R+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is Robert's present age.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+2R ALIGN=MIDDLE  ALT=\"F+=+2R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+2%2824%29 ALIGN=MIDDLE  ALT=\"F+=+2%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+48 ALIGN=MIDDLE  ALT=\"F+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the father's present age.<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+%281%2F2%29F ALIGN=MIDDLE  ALT=\"R+=+%281%2F2%29F\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+=+%281%2F2%29%2848%29 ALIGN=MIDDLE  ALT=\"24+=+%281%2F2%29%2848%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+=+24 ALIGN=MIDDLE  ALT=\"24+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" > OK, and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R-12+=+%281%2F3%29%28F-12%29 ALIGN=MIDDLE  ALT=\"R-12+=+%281%2F3%29%28F-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=24-12+=+%281%2F3%29%2848-12%29 ALIGN=MIDDLE  ALT=\"24-12+=+%281%2F3%29%2848-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+%281%2F3%29%2836%29 ALIGN=MIDDLE  ALT=\"12+=+%281%2F3%29%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+12 ALIGN=MIDDLE  ALT=\"12+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );