document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=956013>Question 956013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The age of a father is triple the son. 5 years later the product of their ages will be 1000. Find their present ages.<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 #584049 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=584049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> F=father's age; S=son's age<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F=3S ALIGN=MIDDLE  ALT=\"F=3S\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28F%2B5%29%28S%2B5%29=1000 ALIGN=MIDDLE  ALT=\"%28F%2B5%29%28S%2B5%29=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute for F.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283S%2B5%29%28S%2B5%29=1000 ALIGN=MIDDLE  ALT=\"%283S%2B5%29%28S%2B5%29=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3S%5E2%2B20S%2B25=1000 ALIGN=MIDDLE  ALT=\"3S%5E2%2B20S%2B25=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1000 from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3S%5E2%2B20S-975=0 ALIGN=MIDDLE  ALT=\"3S%5E2%2B20S-975=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aS%5E2%2BbS%2Bc=0 ALIGN=MIDDLE  ALT=\"aS%5E2%2BbS%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3S%5E2%2B20S%2B-975+=+0 ALIGN=MIDDLE  ALT=\"3S%5E2%2B20S%2B-975+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"S%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2820%29%5E2-4%2A3%2A-975=12100 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2820%29%5E2-4%2A3%2A-975=12100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=12100 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-20%2B-sqrt%28+12100+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-20%2B-sqrt%28+12100+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B1%5D+=+%28-%2820%29%2Bsqrt%28+12100+%29%29%2F2%5C3+=+15 ALIGN=MIDDLE  ALT=\"S%5B1%5D+=+%28-%2820%29%2Bsqrt%28+12100+%29%29%2F2%5C3+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B2%5D+=+%28-%2820%29-sqrt%28+12100+%29%29%2F2%5C3+=+-21.6666666666667 ALIGN=MIDDLE  ALT=\"S%5B2%5D+=+%28-%2820%29-sqrt%28+12100+%29%29%2F2%5C3+=+-21.6666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3S%5E2%2B20S%2B-975 ALIGN=MIDDLE  ALT=\"3S%5E2%2B20S%2B-975\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3S%5E2%2B20S%2B-975+=+3%28S-15%29%2A%28S--21.6666666666667%29 ALIGN=MIDDLE  ALT=\"3S%5E2%2B20S%2B-975+=+3%28S-15%29%2A%28S--21.6666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 15, -21.6666666666667.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B20%2Ax%2B-975+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B20%2Ax%2B-975+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "So S=15 ANSWER 1: The son is 15 years old.<BR>\n" );
document.write( "F=3S=3(15yrs)=45yrs ANSWER 2: The father is 45 years old.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28F%2B5%29%28S%2B5%29=1000 ALIGN=MIDDLE  ALT=\"%28F%2B5%29%28S%2B5%29=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2845%2B5%29%2815%2B5%29=1000 ALIGN=MIDDLE  ALT=\"%2845%2B5%29%2815%2B5%29=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850%29%2820%29=1000 ALIGN=MIDDLE  ALT=\"%2850%29%2820%29=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=1000 ALIGN=MIDDLE  ALT=\"1000=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );