document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997500>Question 997500</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this..: Food A has 560 calories per pound and 80 units of vitamins per pound, Food B has a 240 calories per pound and 400 units of vitamins per pound, and food C has 480 calories per pound and 160 units of vitamins per pound. It is desired to have a 10-lb mixture of foods A,B,and C to contain a total of 2000 calories and 1200 units of vitamins. Show that these requirements lead to an inconsistent system of equations, and therefore the mixture in not possible. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615581 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615581\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = number of pounds of A.<BR>\n" );
document.write( "let b = number of pounds of B.<BR>\n" );
document.write( "let c = number of pounds of C.\r<BR>\n" );
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document.write( "you get 3 equations that need to be solved simultaneoulsy.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "a + b + c = 10 = total number of pounds.<BR>\n" );
document.write( "560 a + 240b + 480c = 2000 = total number of calories.<BR>\n" );
document.write( "80a + 400b + 160c = 1200 = total units of vitamins.\r<BR>\n" );
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document.write( "the calculartions are shown below:\r<BR>\n" );
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document.write( "in 1 we write the equations as shown above.\r<BR>\n" );
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document.write( "in 2 we multiply the first equation by 560 and subtract the second equation from that to get 320b + 80c = 3600\r<BR>\n" );
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document.write( "in 3 we multiply the first equation by 80 and subtract the first equation from the third equation to get 320b + 80c = 400\r<BR>\n" );
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document.write( "in 4 we subtract 320b + 80c = 400 from 320b + 80c = 3600 to get 0 + 0 = 3200\r<BR>\n" );
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document.write( "we are left with 0 = 3200 which is not true and so there is no common solution to these 3 equations.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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