document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163244>Question 1163244</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi\r<BR>\n" );
document.write( "\n" );
document.write( "The sum of the ages of Ruth Selma and Tom is one year more than 3 times toms age.the sum of Tom and Selma ages is 2 years more than 3 times Ruth's age.<BR>\n" );
document.write( "The sum of Ruth and toms ages is the same as the sum of selmas age and half of ruths age.  How old is each one.\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #787269 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=787269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -----------------------------------------------------------------<BR>\n" );
document.write( "The sum of the ages of Ruth Selma and Tom is one year more than 3 times toms age.the sum of Tom and Selma ages is 2 years more than 3 times Ruth's age.<BR>\n" );
document.write( "The sum of Ruth and toms ages is the same as the sum of selmas age and half of ruths age.<BR>\n" );
document.write( "------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Ruth        r\r\n" );
document.write( "Selma       x\r\n" );
document.write( "Tom         t\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28r%2Bx%2Bt=1%2B3t%2Cx%2Bt=2%2B3r%2Cr%2Bt=x%2Br%2F2%29 ALIGN=MIDDLE  ALT=\"system%28r%2Bx%2Bt=1%2B3t%2Cx%2Bt=2%2B3r%2Cr%2Bt=x%2Br%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "-\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28r%2Bx-2t=1%2C-3r%2Bx%2Bt=2%2C2r%2B2t=2x%2Br%29 ALIGN=MIDDLE  ALT=\"system%28r%2Bx-2t=1%2C-3r%2Bx%2Bt=2%2C2r%2B2t=2x%2Br%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28r%2Bx-2t=1%2C3r-x-t=-2%2Cr-2x%2B2t=0%29 ALIGN=MIDDLE  ALT=\"system%28r%2Bx-2t=1%2C3r-x-t=-2%2Cr-2x%2B2t=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From here or earlier, methods can vary, but choosing E1+E3, this gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r-x=1 ALIGN=MIDDLE  ALT=\"2r-x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This means, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2r-1 ALIGN=MIDDLE  ALT=\"x=2r-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substituting for the expression for x,\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28r%2B2r-1-2t=1%2C3r-2r%2B1-t=-2%2Cr-2%282r-1%29%2B2t=0%29 ALIGN=MIDDLE  ALT=\"system%28r%2B2r-1-2t=1%2C3r-2r%2B1-t=-2%2Cr-2%282r-1%29%2B2t=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283r-2t=2%2Cr-t=-3%2Cr-4r%2B2%2B2t=0%29 ALIGN=MIDDLE  ALT=\"system%283r-2t=2%2Cr-t=-3%2Cr-4r%2B2%2B2t=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283r-2t=2%2Cr-t=-3%2C-3r%2B2t=-2%29 ALIGN=MIDDLE  ALT=\"system%283r-2t=2%2Cr-t=-3%2C-3r%2B2t=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------------here, E1 and E3 are equivalent, so,...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283r-2t=2%2Cr-t=-3%29 ALIGN=MIDDLE  ALT=\"system%283r-2t=2%2Cr-t=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );