document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697142>Question 697142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mary Lou is 4 years younger than her sister, Jane. Their mother, who is a mathematics teacher, noticed that the product of the ages of the two sisters is 32. How old are the girls?\r<BR>\n" );
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document.write( "So far i have : y= age of jane<BR>\n" );
document.write( "                x= age of mary lu\r<BR>\n" );
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document.write( "y-x<BR>\n" );
document.write( "y(x)=32  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429687 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=429687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, you are on the right track but the trick is that there are two equations.<BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "Y = Age of Jane<BR>\n" );
document.write( "X = Age of Mary Lou<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Setup:<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+X+%2B+4 ALIGN=MIDDLE  ALT=\"Y+=+X+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+%2A+X+=+32 ALIGN=MIDDLE  ALT=\"Y+%2A+X+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Since equation 1 is already solved for Y, plug (X + 4) into equation 2 for Y.<BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+%2A+X+=+32 ALIGN=MIDDLE  ALT=\"Y+%2A+X+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28X+%2B+4%29%2AX+=+32 ALIGN=MIDDLE  ALT=\"%28X+%2B+4%29%2AX+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+%2B+4X+=+32 ALIGN=MIDDLE  ALT=\"X%5E2+%2B+4X+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 32 from both sides to set the equation equal to zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+%2B+4X+-+32+=+0 ALIGN=MIDDLE  ALT=\"X%5E2+%2B+4X+-+32+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can now factor the equation or use the quadratic equation.<BR>\n" );
document.write( "Here is the quadratic equation approach.<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=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=1X%5E2%2B4X%2B-32+=+0 ALIGN=MIDDLE  ALT=\"1X%5E2%2B4X%2B-32+=+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=%284%29%5E2-4%2A1%2A-32=144 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284%29%5E2-4%2A1%2A-32=144\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=144 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+=+%28-4%2B-sqrt%28+144+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-4%2B-sqrt%28+144+%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-%284%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+4 ALIGN=MIDDLE  ALT=\"X%5B1%5D+=+%28-%284%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+4\"   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-%284%29-sqrt%28+144+%29%29%2F2%5C1+=+-8 ALIGN=MIDDLE  ALT=\"X%5B2%5D+=+%28-%284%29-sqrt%28+144+%29%29%2F2%5C1+=+-8\"   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=1X%5E2%2B4X%2B-32 ALIGN=MIDDLE  ALT=\"1X%5E2%2B4X%2B-32\"   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=1X%5E2%2B4X%2B-32+=+1%28X-4%29%2A%28X--8%29 ALIGN=MIDDLE  ALT=\"1X%5E2%2B4X%2B-32+=+1%28X-4%29%2A%28X--8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4, -8.\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+1%2Ax%5E2%2B4%2Ax%2B-32+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-32+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "So X is 4 or -8.<BR>\n" );
document.write( "Since age is a positive number this means that Mary Lou is 4<BR>\n" );
document.write( "Now plug 4 into equation 1 for X to solve for Jane's age<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+X+%2B+4 ALIGN=MIDDLE  ALT=\"Y+=+X+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+%284%29+%2B+4 ALIGN=MIDDLE  ALT=\"Y+=+%284%29+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28Y+=+8%29 ALIGN=MIDDLE  ALT=\"highlight%28Y+=+8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );