document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113120>Question 113120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Helen's age next year will be three times Dan's age last year.  Their present ages total 32.  How old is each now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82358 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This year Helen is h years old, and Dan is d years old.  Helen's age next year then must be h + 1.  And Dan's age last year must have been d - 1.  The problem tells us:\r<BR>\n" );
document.write( "\n" );
document.write( "Helen's age next year (h + 1) will be (=) 3 times Dan's age last year 3(d - 1).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we can write:<BR>\n" );
document.write( "Eq. 1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2B1=3%28d-1%29 ALIGN=MIDDLE  ALT=\"h%2B1=3%28d-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We also know that their present ages, h and d, total 32, so we can write:<BR>\n" );
document.write( "Eq. 2)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Bd=32 ALIGN=MIDDLE  ALT=\"h%2Bd=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Start by solving Eq. 2) for one of the variables (doesn't matter which, I'll choose to solve for h)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=32-d ALIGN=MIDDLE  ALT=\"h=32-d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Adding -d to both sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now we have an expression that represents h in terms of d that can be substituted into Eq. 1), thus:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2832-d%29%2B1=3%28d-1%29 ALIGN=MIDDLE  ALT=\"%2832-d%29%2B1=3%28d-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, simplify and solve for d:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33-d=3d-3 ALIGN=MIDDLE  ALT=\"33-d=3d-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Distributive and Associative Properties<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-d-3d=-3-33 ALIGN=MIDDLE  ALT=\"-d-3d=-3-33\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Adding -3d and -33 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4d=-36 ALIGN=MIDDLE  ALT=\"-4d=-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Collecting terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-36%2F-4=9 ALIGN=MIDDLE  ALT=\"d=-36%2F-4=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -4, and now we know that this year, Dan is 9.  Since the sum of their ages is 32, Helen must be 32 - 9 = 23.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's check the answer.\r<BR>\n" );
document.write( "\n" );
document.write( "Helen's age next year will be 24.  Dan's age last year was 8.  3 times 8 is 24.  Furthermore, 9 + 23 = 32.  So our numbers satisfy both of the conditions of the problem.  Answer checks.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hope that helps,<BR>\n" );
document.write( "John\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );