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" );
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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 #473790 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=473790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let father's and daughter's age be x and y years respectively now.\r<BR>\n" );
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document.write( "Now:<BR>\n" );
document.write( "xy = 430 ________ (1)\r<BR>\n" );
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document.write( "3 years before:<BR>\n" );
document.write( "x - 3 = 4y<BR>\n" );
document.write( "x = 4y + 3 ________ (2)\r<BR>\n" );
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document.write( "Substituting x from (2) into (1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y+%2B+3%29y+=+430 ALIGN=MIDDLE  ALT=\"%284y+%2B+3%29y+=+430\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2%2B3y-430=0 ALIGN=MIDDLE  ALT=\"4y%5E2%2B3y-430=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve this equation to find y<BR>\n" );
document.write( "<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=ay%5E2%2Bby%2Bc=0 ALIGN=MIDDLE  ALT=\"ay%5E2%2Bby%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2%2B3y%2B430+=+0 ALIGN=MIDDLE  ALT=\"4y%5E2%2B3y%2B430+=+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=y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"y%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=%283%29%5E2-4%2A4%2A430=-6871 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A4%2A430=-6871\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -6871 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -6871 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+6871%29+=+82.8914953418021 ALIGN=MIDDLE  ALT=\"sqrt%28+6871%29+=+82.8914953418021\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B12%5D+=+%28-3%2B-+i%2Asqrt%28+-6871+%29%29%2F2%5C4+=++%28-3%2B-+i%2A82.8914953418021%29%2F2%5C4+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\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%2B3%2Ax%2B430+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B430+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "Imaginary roots suggest that this is impossible. Check and ensure that the data for the question is correct. </SPAN>\n" );
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