document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=567656>Question 567656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> marilyn is three years younger than her friend rosie. in seven years the product of their ages will be 2 less than six times the product of their ages five years ago. how ald are each at present </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #366662 by </B><A HREF=/tutors/aboutme.mpl?userid=Maths68><B>Maths68(1474)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Maths68><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=Maths68><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=366662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let<BR>\n" );
document.write( "Present age of Marilyn = m<BR>\n" );
document.write( "Present age of Rosie = r\r<BR>\n" );
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document.write( "Marilyn is three years younger than her friend Rosie<BR>\n" );
document.write( "m=r-3..............(1)\r<BR>\n" );
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document.write( "Five years ago<BR>\n" );
document.write( "Age of Marilyn was = m-5<BR>\n" );
document.write( "Age of Rosie was = r-5\r<BR>\n" );
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document.write( "In seven years<BR>\n" );
document.write( "Age of Marilyn will be = m+7<BR>\n" );
document.write( "Age of Rosie will be = r+7\r<BR>\n" );
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document.write( "THEN\r<BR>\n" );
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document.write( "In seven years the product of their ages will be 2 less than six times the product of their ages five years ago.\r<BR>\n" );
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document.write( "(m+7)(r+7)=6[(m-5)(r-5)]-2<BR>\n" );
document.write( "mr+7m+7r+49=6(mr-5m-5r+25)-2<BR>\n" );
document.write( "mr+7m+7r+49=6mr-30m-30r+150-2<BR>\n" );
document.write( "mr-6mr+7m+30m+30r+7r=150-2-49<BR>\n" );
document.write( "-5mr+37m+37r=150-51<BR>\n" );
document.write( "-5mr+37m+37r=99..................(2)\r<BR>\n" );
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document.write( "Put the value of m from (1) to (2)<BR>\n" );
document.write( "-5(r-3)r+37(r-3)+37r=99<BR>\n" );
document.write( "-5r^2+15r+37r-111+37r=99<BR>\n" );
document.write( "-5r^2+89r-99-111=0<BR>\n" );
document.write( "-5r^2+89r-200=0<BR>\n" );
document.write( "Now solve for 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=ar%5E2%2Bbr%2Bc=0 ALIGN=MIDDLE  ALT=\"ar%5E2%2Bbr%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5r%5E2%2B89r%2B-210+=+0 ALIGN=MIDDLE  ALT=\"-5r%5E2%2B89r%2B-210+=+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=r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"r%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=%2889%29%5E2-4%2A-5%2A-210=3721 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2889%29%5E2-4%2A-5%2A-210=3721\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3721 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+=+%28-89%2B-sqrt%28+3721+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-89%2B-sqrt%28+3721+%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=r%5B1%5D+=+%28-%2889%29%2Bsqrt%28+3721+%29%29%2F2%5C-5+=+2.8 ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+%28-%2889%29%2Bsqrt%28+3721+%29%29%2F2%5C-5+=+2.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+%28-%2889%29-sqrt%28+3721+%29%29%2F2%5C-5+=+15 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+%28-%2889%29-sqrt%28+3721+%29%29%2F2%5C-5+=+15\"   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=-5r%5E2%2B89r%2B-210 ALIGN=MIDDLE  ALT=\"-5r%5E2%2B89r%2B-210\"   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=-5r%5E2%2B89r%2B-210+=+-5%28r-2.8%29%2A%28r-15%29 ALIGN=MIDDLE  ALT=\"-5r%5E2%2B89r%2B-210+=+-5%28r-2.8%29%2A%28r-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.8, 15.\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+-5%2Ax%5E2%2B89%2Ax%2B-210+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B89%2Ax%2B-210+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "r=15 or r = 2.8 (reject)\r<BR>\n" );
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document.write( "Put r=15 in (1)<BR>\n" );
document.write( "m=r-3<BR>\n" );
document.write( "m=15-3<BR>\n" );
document.write( "m=12\r<BR>\n" );
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document.write( "Present age of Marilyn = m = 12 years old<BR>\n" );
document.write( "Present age of Rosie = r = 15 years old\r<BR>\n" );
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document.write( "Check<BR>\n" );
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document.write( "Five years ago<BR>\n" );
document.write( "Age of Marilyn was = 7<BR>\n" );
document.write( "Age of Rosie was = 10\r<BR>\n" );
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document.write( "In seven years<BR>\n" );
document.write( "Age of Marilyn will be = 19<BR>\n" );
document.write( "Age of Rosie will be = 22\r<BR>\n" );
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document.write( "THEN\r<BR>\n" );
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document.write( "In seven years the product of their ages will be 2 less than six times the product of their ages five years ago.\r<BR>\n" );
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document.write( "19*22=6(7*10)-2<BR>\n" );
document.write( "418=6(70)-2<BR>\n" );
document.write( "418=420-2<BR>\n" );
document.write( "418=418\r<BR>\n" );
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document.write( " </SPAN>\n" );
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