document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891813>Question 891813</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi is there a way of working out how many 3 course meals and 2 course meals (single courses must be calculated as a three course) from the value of starters, mains and desserts given to a table?\r<BR>\n" );
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document.write( "For example, a table has 10 starters, 12 mains and 8 desserts, is there an equation that can be used to calculate how many 2 course and 3 course options were given at the table?\r<BR>\n" );
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document.write( "I hope this makes sense and that it is possible.\r<BR>\n" );
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document.write( "Thanks<BR>\n" );
document.write( "Simon  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #540050 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=540050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is included in a two course meal? <BR>\n" );
document.write( "starts and main?<BR>\n" );
document.write( "main and dessert?<BR>\n" );
document.write( "Under these circumstances we have three unknowns and three equations<BR>\n" );
document.write( "w= three course<BR>\n" );
document.write( "x= starters and main<BR>\n" );
document.write( "y= main and dessert\r<BR>\n" );
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document.write( "w+x+0*y=10<BR>\n" );
document.write( "w+0*x+y=8<BR>\n" );
document.write( "w+x+y=12\r<BR>\n" );
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document.write( "1,1,0,10<BR>\n" );
document.write( "1,0,1,8<BR>\n" );
document.write( "1,1,1,12\r<BR>\n" );
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document.write( "add  down (-1/1) *row 1 to row 2<BR>\n" );
document.write( "1,1,0,10<BR>\n" );
document.write( "0,-1,1,-2<BR>\n" );
document.write( "1,1,1,12\r<BR>\n" );
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document.write( "add  down (-1/1) *row 1 to row 3<BR>\n" );
document.write( "1,1,0,10<BR>\n" );
document.write( "0,-1,1,-2<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
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document.write( "divide row 2 by -1/1<BR>\n" );
document.write( "1,1,0,10<BR>\n" );
document.write( "0,1,-1,2<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
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document.write( "add  down (0/1) *row 2 to row 3<BR>\n" );
document.write( "1,1,0,10<BR>\n" );
document.write( "0,1,-1,2<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
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document.write( "We now have the value for the last variable.<BR>\n" );
document.write( "We will work our way up and get the other solutions.\r<BR>\n" );
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document.write( "add up  (1/1) *row 3 to row 2<BR>\n" );
document.write( "1,1,0,10<BR>\n" );
document.write( "0,1,0,4<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (0/1) *row 3 to row 1<BR>\n" );
document.write( "1,1,0,10<BR>\n" );
document.write( "0,1,0,4<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1/1) *row 2 to row 1<BR>\n" );
document.write( "1,0,0,6<BR>\n" );
document.write( "0,1,0,4<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
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document.write( "final<BR>\n" );
document.write( "1,0,0,6<BR>\n" );
document.write( "0,1,0,4<BR>\n" );
document.write( "0,0,1,2\r<BR>\n" );
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document.write( "6 three course <BR>\n" );
document.write( "4 starters and main<BR>\n" );
document.write( "2 main and dessert<BR>\n" );
document.write( "10 starters<BR>\n" );
document.write( "12 main<BR>\n" );
document.write( "8 dessert\r<BR>\n" );
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document.write( "\"6\",\"4\",\"2\"<BR>\n" );
document.write( "(6,4,2)<BR>\n" );
document.write( " </SPAN>\n" );
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