document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=287596>Question 287596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hannah, Mark and Tom have a combined age of 68. Hannah is twice as old as the difference between Mark and Tom's age. Mark and Tom's combined age is 16 times<BR>\n" );
document.write( "Hannah's age. Mark is older than Tom. How old is Tom?\r<BR>\n" );
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document.write( "(a) 31 (b) 32 (c) 33 (d) 34 (e) None of the above\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208446 by </B><A HREF=/tutors/aboutme.mpl?userid=Deina><B>Deina(147)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Deina><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=Deina><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=208446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's put this in a form where we can see what we're looking for:<ul><BR>\n" );
document.write( "<li>Hannah, Mark and Tom have a combined age of 68. So:<BR>\n" );
document.write( "H + M + T = 68<br><BR>\n" );
document.write( "<li>Hannah is twice as old as the difference between Mark and Tom's age. <BR>\n" );
document.write( "H = 2(|M - T|)<br><BR>\n" );
document.write( "<li>Mark and Tom's combined age is 16 times Hannah's age.<BR>\n" );
document.write( "M + T = 16(H) <br><BR>\n" );
document.write( "<li>Mark is older than Tom.</ul><BR>\n" );
document.write( "Now we have a series of equations that we can solve:<BR>\n" );
document.write( "H + M + T = 68<BR>\n" );
document.write( "H = 2(M - T)<BR>\n" );
document.write( "M + T = 16(H)<br><BR>\n" );
document.write( "The 1st thing that I see is the similarity between the 1st & 3rd equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+H+%2B+M+%2B+T+=+68+ ALIGN=MIDDLE  ALT=\"+H+%2B+M+%2B+T+=+68+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+M+%2B+T+=+16%28H%29 ALIGN=MIDDLE  ALT=\"+M+%2B+T+=+16%28H%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28H+%2B+M+%2B+T%29-+H+=+68+-+H+ ALIGN=MIDDLE  ALT=\"+%28H+%2B+M+%2B+T%29-+H+=+68+-+H+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract H from both sides, giving us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+M+%2B+T+=+68+-+H+ ALIGN=MIDDLE  ALT=\"+M+%2B+T+=+68+-+H+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br> and from the 3rd equation we know that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+M+%2B+T+=+16%28H%29 ALIGN=MIDDLE  ALT=\"+M+%2B+T+=+16%28H%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16%28H%29+=+68+-+H+ ALIGN=MIDDLE  ALT=\"+16%28H%29+=+68+-+H+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add H to each side and:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+17%28H%29+=+68+ ALIGN=MIDDLE  ALT=\"+17%28H%29+=+68+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br> Divide both sides by 17 and we find that:<BR>\n" );
document.write( "<b>H = 4 So Hannah is 4 years old.</b> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+M+%2B+T+=+68+-+H+ ALIGN=MIDDLE  ALT=\"+M+%2B+T+=+68+-+H+\"   DISABLED_style= \"max-width:90%; height:auto;\" > So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+M+%2B+T+=+64+ ALIGN=MIDDLE  ALT=\"+M+%2B+T+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the 4th clue we know that Mark is older than Tom, and from the 2nd equation we know that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2F2+=+%282%28M+-+T%29%29%2F2+ ALIGN=MIDDLE  ALT=\"+4%2F2+=+%282%28M+-+T%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+=+M+-+T+ ALIGN=MIDDLE  ALT=\"+2+=+M+-+T+\"   DISABLED_style= \"max-width:90%; height:auto;\" >we now know that the difference between Mark & Tom's age is <b>2</b> years<br><BR>\n" );
document.write( "So taking our <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+M+%2B+T+=+64+ ALIGN=MIDDLE  ALT=\"+M+%2B+T+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will substitute Tom's age + 2 for Marks age (and reverse their order, just to clarify things):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+%2B+T+%2B+2+=+64+ ALIGN=MIDDLE  ALT=\"+T+%2B+T+%2B+2+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2T+%2B+2+=+64+ ALIGN=MIDDLE  ALT=\"+2T+%2B+2+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2 from each side, then divide each side: <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2T%2F2+=+62%2F2+ ALIGN=MIDDLE  ALT=\"+2T%2F2+=+62%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <b>Tom is 31</b> years old, making <b>Mark = 33</b> <br><BR>\n" );
document.write( "Substitute those numbers back into the equations to check, reread the problem to make sure you're answering the right question <i>and bob's your uncle!</i>\r<BR>\n" );
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