document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74272>Question 74272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Marivic is five years older than Michelle. In three years, the product of her age and Michelle's age five years ago will be 90 years. Find their present ages. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53371 by </B><A HREF=/tutors/aboutme.mpl?userid=vidhyak><B>vidhyak(98)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vidhyak><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=53371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let Marivic's age be x <BR>\n" );
document.write( "Let Michelle's age be y \r<BR>\n" );
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document.write( "Marivic is five years older than Michelle \r<BR>\n" );
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document.write( "x = y + 5 -----------------------eq. 1 \r<BR>\n" );
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document.write( "In three years, the product of her age and Michelle's age five years ago will be 90 years \r<BR>\n" );
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document.write( "In three years marvic will be x + 3 yrs old <BR>\n" );
document.write( "Michelle's age five years ago was y - 5 yrs old \r<BR>\n" );
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document.write( "(x + 3)(y - 5) = 90 --------------eq 2 \r<BR>\n" );
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document.write( "Substitue eq1 in eq2 \r<BR>\n" );
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document.write( "(y + 5 + 3) (y - 5) = 90 <BR>\n" );
document.write( "(y + 8) (y - 5) = 90 <BR>\n" );
document.write( "y^2 + 3y -40 = 90<BR>\n" );
document.write( "y^2 + 3y -130 = 0\r<BR>\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=1y%5E2%2B3y%2B-130+=+0 ALIGN=MIDDLE  ALT=\"1y%5E2%2B3y%2B-130+=+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%2A1%2A-130=529 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A1%2A-130=529\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=529 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+=+%28-3%2B-sqrt%28+529+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+529+%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=y%5B1%5D+=+%28-%283%29%2Bsqrt%28+529+%29%29%2F2%5C1+=+10 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+%28-%283%29%2Bsqrt%28+529+%29%29%2F2%5C1+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+%28-%283%29-sqrt%28+529+%29%29%2F2%5C1+=+-13 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+%28-%283%29-sqrt%28+529+%29%29%2F2%5C1+=+-13\"   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=1y%5E2%2B3y%2B-130 ALIGN=MIDDLE  ALT=\"1y%5E2%2B3y%2B-130\"   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=1y%5E2%2B3y%2B-130+=+1%28y-10%29%2A%28y--13%29 ALIGN=MIDDLE  ALT=\"1y%5E2%2B3y%2B-130+=+1%28y-10%29%2A%28y--13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 10, -13.\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%2B3%2Ax%2B-130+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-130+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Answers for y= 10,-13\r<BR>\n" );
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document.write( "Age is a positive integer, so Michelle's age is 10\r<BR>\n" );
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document.write( "x = y + 5<BR>\n" );
document.write( "x= 15\r<BR>\n" );
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document.write( "so Marivic's age is 15<BR>\n" );
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