document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79474>Question 79474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This problem I am having alot of trouble trying to figure out. Please Help!!\r<BR>\n" );
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document.write( "Mutt is half as old as Jeff will be when Mutt is twice as old as Jeff was when Mutt was half as old as Jeff is now.  In five years, the sum of Mutt’s and Jeff’s ages will be 100.  How old are Mutt and Jeff now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57084 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Wow! this problem is either pretty tough or I'm just not reading it right.<BR>\n" );
document.write( "Even if I'm off base, you might get something out of my method.<BR>\n" );
document.write( "The thing to watch carefully is the words \"now\" and \"when\" and phrases<BR>\n" );
document.write( "\"will be\" and \"was\".<BR>\n" );
document.write( "Let M = Mutt's age now<BR>\n" );
document.write( "Let J = Jeff's age now<BR>\n" );
document.write( "The problem is saying that Mutt's age now is half of Jeff's age at <BR>\n" );
document.write( "some future time. I'll call that time <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+%2B+a ALIGN=MIDDLE  ALT=\"J+%2B+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a is in years<BR>\n" );
document.write( "So now I've got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+%28J+%2B+a%29+%2F+2 ALIGN=MIDDLE  ALT=\"M+=+%28J+%2B+a%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When Jeff is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+%2B+a ALIGN=MIDDLE  ALT=\"J+%2B+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > years old, Mutt will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+%2B+a ALIGN=MIDDLE  ALT=\"M+%2B+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > years old<BR>\n" );
document.write( "The problem says that Mutt's age then will be twice what Jeffs<BR>\n" );
document.write( "age was at some time in the past. I can now say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+%2B+a+=+2%28J+-+b%29 ALIGN=MIDDLE  ALT=\"M+%2B+a+=+2%28J+-+b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where b are the years to be subtracted from M and J.<BR>\n" );
document.write( "At this time in the past, -b years, what was Mutts age? The problem says<BR>\n" );
document.write( "it was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+-+b+=+J+%2F+2 ALIGN=MIDDLE  ALT=\"M+-+b+=+J+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, half as old as Jeff is now.<BR>\n" );
document.write( "Going back,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+%28J+%2B+a%29+%2F+2 ALIGN=MIDDLE  ALT=\"M+=+%28J+%2B+a%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > What's a in this equation? To find it, solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+%2B+a+=+2%28J+-+b%29 ALIGN=MIDDLE  ALT=\"M+%2B+a+=+2%28J+-+b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2%28J+-+b%29+-+M ALIGN=MIDDLE  ALT=\"a+=+2%28J+-+b%29+-+M\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+%28J+%2B+2%28J+-+b%29+-+M%29+%2F+2 ALIGN=MIDDLE  ALT=\"M+=+%28J+%2B+2%28J+-+b%29+-+M%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2M+=+J+%2B+2J+-+2b+-+M ALIGN=MIDDLE  ALT=\"2M+=+J+%2B+2J+-+2b+-+M\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3M+=+3J+-+2b ALIGN=MIDDLE  ALT=\"3M+=+3J+-+2b\"   DISABLED_style= \"max-width:90%; height:auto;\" > What's b? Use  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+-+b+=+J+%2F+2 ALIGN=MIDDLE  ALT=\"M+-+b+=+J+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+M+-+J%2F2 ALIGN=MIDDLE  ALT=\"b+=+M+-+J%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3M+=+3J+-+2%28M+-+J%2F2%29 ALIGN=MIDDLE  ALT=\"3M+=+3J+-+2%28M+-+J%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3M+=+3J+-+2M+%2B+J ALIGN=MIDDLE  ALT=\"3M+=+3J+-+2M+%2B+J\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5M+=+4J ALIGN=MIDDLE  ALT=\"5M+=+4J\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+4J%2F5 ALIGN=MIDDLE  ALT=\"M+=+4J%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now use the last piece of information<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+%2B+M+%2B+5+=+100 ALIGN=MIDDLE  ALT=\"J+%2B+M+%2B+5+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+%2B+4J%2F5+%2B+5+=+100 ALIGN=MIDDLE  ALT=\"J+%2B+4J%2F5+%2B+5+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9J%2F5+=+95 ALIGN=MIDDLE  ALT=\"9J%2F5+=+95\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+=+52.78 ALIGN=MIDDLE  ALT=\"J+=+52.78\"   DISABLED_style= \"max-width:90%; height:auto;\" > Jeff's age now<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+4J%2F5 ALIGN=MIDDLE  ALT=\"M+=+4J%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+42.22 ALIGN=MIDDLE  ALT=\"M+=+42.22\"   DISABLED_style= \"max-width:90%; height:auto;\" > Mutt's age now<BR>\n" );
document.write( "I plugged the answers back into the equations and they checked,<BR>\n" );
document.write( "but I've been wrong before, so use your judgement.<BR>\n" );
document.write( "  </SPAN>\n" );
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