document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=637069>Question 637069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the following sum the same two numbers are needed.  When they are added or mutliplied together, they form the answers for (a) and (b). I need to work out what theose numbers are\r<BR>\n" );
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document.write( "(a) ............+........... = 2.7<BR>\n" );
document.write( "(b) ............x........... = 1.8\r<BR>\n" );
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document.write( "Can anone help me with the following  I just cnat seem to get it thanks\r<BR>\n" );
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document.write( "I have already submitted this question but my email address was wrong </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401416 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=401416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x and y be the two numbers<BR>\n" );
document.write( "x+y=2.7<BR>\n" );
document.write( "x+y=27/10<BR>\n" );
document.write( "10(x+y)=27<BR>\n" );
document.write( "10x+10y=27.............(1)\r<BR>\n" );
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document.write( "xy=1.8<BR>\n" );
document.write( "xy=18/10<BR>\n" );
document.write( "x=18/10y...............(2)\r<BR>\n" );
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document.write( "Put the value of x from (2) to (1)<BR>\n" );
document.write( "10(18/10y)+10y=27<BR>\n" );
document.write( "18/y+10y=27<BR>\n" );
document.write( "(18+10Y^2)/y=27<BR>\n" );
document.write( "18+10Y^2=27y<BR>\n" );
document.write( "10y^2-27y+18=0<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=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=10x%5E2%2B-27x%2B18+=+0 ALIGN=MIDDLE  ALT=\"10x%5E2%2B-27x%2B18+=+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=%28-27%29%5E2-4%2A10%2A18=9 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-27%29%5E2-4%2A10%2A18=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=9 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--27%2B-sqrt%28+9+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--27%2B-sqrt%28+9+%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-%28-27%29%2Bsqrt%28+9+%29%29%2F2%5C10+=+1.5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+9+%29%29%2F2%5C10+=+1.5\"   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-%28-27%29-sqrt%28+9+%29%29%2F2%5C10+=+1.2 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-27%29-sqrt%28+9+%29%29%2F2%5C10+=+1.2\"   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=10x%5E2%2B-27x%2B18 ALIGN=MIDDLE  ALT=\"10x%5E2%2B-27x%2B18\"   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=10x%5E2%2B-27x%2B18+=+10%28x-1.5%29%2A%28x-1.2%29 ALIGN=MIDDLE  ALT=\"10x%5E2%2B-27x%2B18+=+10%28x-1.5%29%2A%28x-1.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.5, 1.2.\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+10%2Ax%5E2%2B-27%2Ax%2B18+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B-27%2Ax%2B18+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "So<BR>\n" );
document.write( "y=1.5 or 1.2\r<BR>\n" );
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document.write( "Put the values of y in (1)<BR>\n" );
document.write( "10x+10y=27.............(1)<BR>\n" );
document.write( "Put y=1.5<BR>\n" );
document.write( "10x+10(1.5)=27<BR>\n" );
document.write( "10x+15=27<BR>\n" );
document.write( "10x=27-15<BR>\n" );
document.write( "10x=12<BR>\n" );
document.write( "x=12/10<BR>\n" );
document.write( "x=1.2\r<BR>\n" );
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document.write( "Put the values of y in (1)<BR>\n" );
document.write( "10x+10y=27.............(1)<BR>\n" );
document.write( "Put y=1.2<BR>\n" );
document.write( "10x+10(1.2)=27<BR>\n" );
document.write( "10x+12=27<BR>\n" );
document.write( "10x=27-12<BR>\n" );
document.write( "10x=15<BR>\n" );
document.write( "x=15/10<BR>\n" );
document.write( "x=1.5\r<BR>\n" );
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document.write( "So numbers are 1.2 and 1.5\r<BR>\n" );
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document.write( "Check<BR>\n" );
document.write( "=====<BR>\n" );
document.write( "xy=1.8<BR>\n" );
document.write( "(1.2)(1.5)=1.8<BR>\n" );
document.write( "1.8=1.8\r<BR>\n" );
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document.write( "x+y=2.7<BR>\n" );
document.write( "1.2+1.5=2.7<BR>\n" );
document.write( "2.7=2.7 </SPAN>\n" );
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