document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=776905>Question 776905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let the daughter's age be x<BR>\n" );
document.write( "Let the father's age be 4x<BR>\n" );
document.write( "3 years ago: Daughter's age = x-3<BR>\n" );
document.write( "Father's age = 4x-3<BR>\n" );
document.write( "Product of their ages:( x-3)(4x-3)=430<BR>\n" );
document.write( "Opening the bracket and applying quadratic formula method,  we shall have the roots as x= 12.3 and -8.6 <BR>\n" );
document.write( "So, taking the positive value of x= 12.3years.<BR>\n" );
document.write( "Present ages:<BR>\n" );
document.write( "Daughter's (x-3)years = 12.3-3 =9.30years (9 years 3 months)<BR>\n" );
document.write( "Father's age: (4x-3)years= 4×12.3-3 = 46.21years (46 years 2 months 1day)\r<BR>\n" );
document.write( "\n" );
document.write( "Checking:<BR>\n" );
document.write( "9.30×46.21= 429.753 = 430 (approximated) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #473809 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=473809\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3 years ago a father was 4 times as old as his daughter is now. The product of their ages is 430. Calculate their present ages.<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "F*D = 430<BR>\n" );
document.write( "F-3 = 4(D-3)<BR>\n" );
document.write( "F = 4D - 9<BR>\n" );
document.write( "----<BR>\n" );
document.write( "D*(4D-9) = 430<BR>\n" );
document.write( "4D^2 - 9D - 430 = 0<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B-9x%2B-430+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-9x%2B-430+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%28-9%29%5E2-4%2A4%2A-430=6961 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-9%29%5E2-4%2A4%2A-430=6961\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=6961 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--9%2B-sqrt%28+6961+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--9%2B-sqrt%28+6961+%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=x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+6961+%29%29%2F2%5C4+=+11.5540759418081 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+6961+%29%29%2F2%5C4+=+11.5540759418081\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-9%29-sqrt%28+6961+%29%29%2F2%5C4+=+-9.30407594180808 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-9%29-sqrt%28+6961+%29%29%2F2%5C4+=+-9.30407594180808\"   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=4x%5E2%2B-9x%2B-430 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-9x%2B-430\"   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=4x%5E2%2B-9x%2B-430+=+%28x-11.5540759418081%29%2A%28x--9.30407594180808%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-9x%2B-430+=+%28x-11.5540759418081%29%2A%28x--9.30407594180808%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 11.5540759418081, -9.30407594180808.\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+4%2Ax%5E2%2B-9%2Ax%2B-430+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-9%2Ax%2B-430+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "----------------------<BR>\n" );
document.write( "D = x<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Not an integer solution.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );