document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=994596>Question 994596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boy is two years more than twice as old as his mother. The sum of their ages is nine years more than the age of their sister. If the sister is three years younger than the older boy, find the age of each. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #613633 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=613633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b, boy<BR>\n" );
document.write( "m, his mother<BR>\n" );
document.write( "s, sister of boy<BR>\n" );
document.write( "-<BR>\n" );
document.write( "MUST expect <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3Cm ALIGN=MIDDLE  ALT=\"b%3Cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >;\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28b=2%2B2%2Am%2Cb%2Bm=9%2Bs%2Cs=-3%2Bb%29 ALIGN=MIDDLE  ALT=\"system%28b=2%2B2%2Am%2Cb%2Bm=9%2Bs%2Cs=-3%2Bb%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%282m-b=-2%2Cm%2Bb-s=9%2Cb-s=3%29 ALIGN=MIDDLE  ALT=\"system%282m-b=-2%2Cm%2Bb-s=9%2Cb-s=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the last two equations to eliminate s, and have a simpler system.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-s=3-b ALIGN=MIDDLE  ALT=\"-s=3-b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=b-3 ALIGN=MIDDLE  ALT=\"s=b-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Bb-%28b-3%29=9 ALIGN=MIDDLE  ALT=\"m%2Bb-%28b-3%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Bb-b%2B3=9 ALIGN=MIDDLE  ALT=\"m%2Bb-b%2B3=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2B3=9 ALIGN=MIDDLE  ALT=\"m%2B3=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28m=6%29 ALIGN=MIDDLE  ALT=\"highlight%28m=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------?<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Use the middle equation of the system to eliminate m.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Bb-s=9 ALIGN=MIDDLE  ALT=\"m%2Bb-s=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Bb-s=9 ALIGN=MIDDLE  ALT=\"6%2Bb-s=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-s=6 ALIGN=MIDDLE  ALT=\"b-s=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >---------This creates a contradiction.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This result shows b-s=6 and one of the system equations was b-s=3.  They cannot both be part of the system of equations.  One of them may be true, but then this makes the other false.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your problem description is wrong. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );