document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=662667>Question 662667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ivan is three years older than his sister Mary. One-third of Ivan's age is two years less than one-half his sister's age one year ago. Find their age's now. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #412892 by </B><A HREF=/tutors/aboutme.mpl?userid=kevwill><B>kevwill(135)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kevwill><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=kevwill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=412892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think the original solver got this one wrong.  <BR>\n" );
document.write( "Let's let i = Ivan's age and m = Mary's age.  Ivan is 3 years older than Mary, so <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+=+m+%2B+3 ALIGN=MIDDLE  ALT=\"i+=+m+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The next one is a little tricky.  One third of Ivan's age is two years less than one half of his sister's age one year ago.  So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2F3+=+%28m-1%29%2F2+-+2 ALIGN=MIDDLE  ALT=\"i%2F3+=+%28m-1%29%2F2+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To simplify the rest of the solution, let's multiply both sides of the above equation by 6:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A%28i%2F3%29+=+%286%2A%28m-1%29%29%2F2+-+6%2A2 ALIGN=MIDDLE  ALT=\"6%2A%28i%2F3%29+=+%286%2A%28m-1%29%29%2F2+-+6%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ai+=+%286%2Am+-+6%29%2F2+-12 ALIGN=MIDDLE  ALT=\"2%2Ai+=+%286%2Am+-+6%29%2F2+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ai+=+3%2Am+-+3+-+12 ALIGN=MIDDLE  ALT=\"2%2Ai+=+3%2Am+-+3+-+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ai+=+3%2Am+-+15 ALIGN=MIDDLE  ALT=\"2%2Ai+=+3%2Am+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting m+3 for i (from the first equation) gives us<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28m%2B3%29+=+3%2Am+-+15 ALIGN=MIDDLE  ALT=\"2%2A%28m%2B3%29+=+3%2Am+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Am+%2B+6+=+3%2Am+-+15 ALIGN=MIDDLE  ALT=\"2%2Am+%2B+6+=+3%2Am+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 2*m from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Am+%2B+6+-+2%2Am+=+3%2Am+-+15+-+2%2Am ALIGN=MIDDLE  ALT=\"2%2Am+%2B+6+-+2%2Am+=+3%2Am+-+15+-+2%2Am\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+m+-+15 ALIGN=MIDDLE  ALT=\"6+=+m+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 15 to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+%2B+15+=+m+-+15+%2B+15 ALIGN=MIDDLE  ALT=\"6+%2B+15+=+m+-+15+%2B+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21+=+m ALIGN=MIDDLE  ALT=\"21+=+m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So Mary is 21 and Ivan is 24.\r<BR>\n" );
document.write( "\n" );
document.write( "We can check our answer by inserting our values for i and m into the original second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F3+=+%2821+-+1%29%2F2+-+2 ALIGN=MIDDLE  ALT=\"24%2F3+=+%2821+-+1%29%2F2+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+20%2F2+-+2 ALIGN=MIDDLE  ALT=\"8+=+20%2F2+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+10+-+2 ALIGN=MIDDLE  ALT=\"8+=+10+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+8 ALIGN=MIDDLE  ALT=\"8+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So our calculations are correct.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );