document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697110>Question 697110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A father says to his son that at the time of his birth he was 3 times older than him. If now father's present age is 18 years, then what was the age of son 4 years  ago?<BR>\n" );
document.write( "ANS: 8 years. But how? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429666 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=429666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There has to be a typo. A father that young sound unreasonable, and the math results in ages that are not integers.<BR>\n" );
document.write( " <BR>\n" );
document.write( "WHAT SHOULD HAVE BEEN:<BR>\n" );
document.write( "The father's present age is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" > years.<BR>\n" );
document.write( "That can be solved as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = age of the son 4 years ago<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = age of the son now.<BR>\n" );
document.write( "The equation can be set up all at one as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B4%29%2B%28x%2B4%29=48 ALIGN=MIDDLE  ALT=\"3%28x%2B4%29%2B%28x%2B4%29=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Going slower, to show the rationale:<BR>\n" );
document.write( "The son's current age is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > years.<BR>\n" );
document.write( "The father says \"I was 3 times as old as that when my son was born.\"<BR>\n" );
document.write( "That means that the father was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B4%29=3x%2B12 ALIGN=MIDDLE  ALT=\"3%28x%2B4%29=3x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > when his son was born.<BR>\n" );
document.write( "Since that was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > years ago,<BR>\n" );
document.write( "now the father must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B12%2B%28x%2B4%29 ALIGN=MIDDLE  ALT=\"3x%2B12%2B%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > years old.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B12%2B%28x%2B4%29=3x%2B12%2Bx%2B4=4x%2B16 ALIGN=MIDDLE  ALT=\"3x%2B12%2B%28x%2B4%29=3x%2B12%2Bx%2B4=4x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B16=48 ALIGN=MIDDLE  ALT=\"4x%2B16=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B16-16=48-16 ALIGN=MIDDLE  ALT=\"4x%2B16-16=48-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=32 ALIGN=MIDDLE  ALT=\"4x=32\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=32%2F4 ALIGN=MIDDLE  ALT=\"x=32%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=8%29 ALIGN=MIDDLE  ALT=\"highlight%28x=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "THE PROBLEM AS POSTED<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = age of the son 4 years ago<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = age of the son now<BR>\n" );
document.write( "The equation that results is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B4%29%2B%28x%2B4%29=18 ALIGN=MIDDLE  ALT=\"3%28x%2B4%29%2B%28x%2B4%29=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It simplifies as before<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B4%29%2B%28x%2B4%29=18 ALIGN=MIDDLE  ALT=\"3%28x%2B4%29%2B%28x%2B4%29=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B12%2B%28x%2B4%29=18 ALIGN=MIDDLE  ALT=\"3x%2B12%2B%28x%2B4%29=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B12%2Bx%2B4=18 ALIGN=MIDDLE  ALT=\"3x%2B12%2Bx%2B4=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B16=18 ALIGN=MIDDLE  ALT=\"4x%2B16=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It solves as before<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B16=18 ALIGN=MIDDLE  ALT=\"4x%2B16=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B16-16=18-16 ALIGN=MIDDLE  ALT=\"4x%2B16-16=18-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=2 ALIGN=MIDDLE  ALT=\"4x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That would make the son <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%261%2F2 ALIGN=MIDDLE  ALT=\"4%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > years old now.<BR>\n" );
document.write( "But it does not make sense to say that the son was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > year old four years ago (we would say he was just 6 months old)<BR>\n" );
document.write( "While the son may proudly be saying \"I am four and a half years old now,\"<BR>\n" );
document.write( "I would call that being just 4 years old, because age is usually stated as the age at the latest birthday, without fractions.<BR>\n" );
document.write( "Furthermore, the father saying \"I was 3 times as old when you were born\" could mean<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%284%29=12 ALIGN=MIDDLE  ALT=\"3%284%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > years old, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%284%261%2F2%29=13%261%2F2 ALIGN=MIDDLE  ALT=\"3%284%261%2F2%29=13%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > years old (if we accept fractional ages),<BR>\n" );
document.write( "and either way that would be too young. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );