document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=852410>Question 852410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A mother is three times as old as her daughter. Four years ago the product of their ages was 256. Find their current ages. Would the equation be (3x-4)(x-4)=256? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #513331 by </B><A HREF=/tutors/aboutme.mpl?userid=pmesler><B>pmesler(52)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=pmesler><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=pmesler><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=513331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the daughter's age  = x\r<BR>\n" );
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document.write( "Let the mother's age = 3x \r<BR>\n" );
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document.write( "The product of their ages is 256. In other words\r<BR>\n" );
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document.write( "(3x-4)(x-4) = 256\r<BR>\n" );
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document.write( "Use FOIL to simplify.\r<BR>\n" );
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document.write( "3x^2-16x+16 = 256 \r<BR>\n" );
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document.write( "Subtract 256 from both sides to make this a quadratic equation. \r<BR>\n" );
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document.write( "3x^2-16x-240 = 0\r<BR>\n" );
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document.write( "Solve for x using the quadratic equation. <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=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=3x%5E2%2B-16x%2B-240+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-16x%2B-240+=+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" );
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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" );
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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=%28-16%29%5E2-4%2A3%2A-240=3136 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-16%29%5E2-4%2A3%2A-240=3136\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3136 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--16%2B-sqrt%28+3136+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--16%2B-sqrt%28+3136+%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-%28-16%29%2Bsqrt%28+3136+%29%29%2F2%5C3+=+12 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+3136+%29%29%2F2%5C3+=+12\"   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-%28-16%29-sqrt%28+3136+%29%29%2F2%5C3+=+-6.66666666666667 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-16%29-sqrt%28+3136+%29%29%2F2%5C3+=+-6.66666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B-16x%2B-240 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-16x%2B-240\"   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=3x%5E2%2B-16x%2B-240+=+3%28x-12%29%2A%28x--6.66666666666667%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-16x%2B-240+=+3%28x-12%29%2A%28x--6.66666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 12, -6.66666666666667.\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%2B-16%2Ax%2B-240+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-16%2Ax%2B-240+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "From this you can see that x = (-6.66,0) and x = (12,0). Obviously we can disregard x = -6.66 since you can't have a negative age. That means that the daughter is 12 years old and her mother is 36 years old.\r<BR>\n" );
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document.write( "Let's plug in these values of x to see if the original equation checks out.\r<BR>\n" );
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document.write( "(3(12)-4)(12-4) = 256\r<BR>\n" );
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document.write( "32 * 8 = 256 \r<BR>\n" );
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document.write( "It checks out so those are the correct ages. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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