document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992432>Question 992432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CAN ANY ONE SOLVE IT BY GAUSSIAN ELIMINATION METHOD?<BR>\n" );
document.write( "A blending process is to combine three components in such a way as to create a final blend of 60000 gallons.The three components  cost $2.00,$1.50 and $1.25 per gallon respectively.Total cost of components should equal $90000.Another requirement in the blending is that the number of gallon  used of component 1 should be twice the amount  used of component 3.determine whether there is a combination of the three components which will lead to a final blend of 60000 gallon costing $90000 and satisfying the blending restrictions<BR>\n" );
document.write( "kindly help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612083 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=612083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A few details are described imprecisely but you have components to be mixed, in quantities x, y, and z for components 1, 2, and 3; in the order listed for the prices of each.\r<BR>\n" );
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document.write( "Accounting for material volumes, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=60000 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=60000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Accounting for material costs,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1.5y%2B1.25z=90000 ALIGN=MIDDLE  ALT=\"2x%2B1.5y%2B1.25z=90000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You would want integer coefficients if possible, so multiply members by 4...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6y%2B5z=360000 ALIGN=MIDDLE  ALT=\"8x%2B6y%2B5z=360000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Part of the description makes  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fz=2 ALIGN=MIDDLE  ALT=\"x%2Fz=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, giving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2z ALIGN=MIDDLE  ALT=\"x=2z\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The system of equations that can be best formed is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By%2Bz=60000%2C8x%2B6y%2B5z=360000%2Cx-2z=0%29 ALIGN=MIDDLE  ALT=\"system%28x%2By%2Bz=60000%2C8x%2B6y%2B5z=360000%2Cx-2z=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You could solve this using your gaussian or gauss-jordan row elimination method, but I wouldn't want to; I'd rather use the x=2z substitution and solve the resulting simpler system.\r<BR>\n" );
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document.write( "As the matrix, you can begin with  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C60000%2C%0D%0A8%2C6%2C5%2C360000%2C%0D%0A1%2C0%2C-2%2C0%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I started solving on paper with pencil, and I am finding a meaningless result as one of the rows, like  ( 0 0 -3 0 ), indicating   z=0.  If my row operations are all correct, this would indicate that your materials can not all three be used to prepare the mixture described in your description. </SPAN>\n" );
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