document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203031>Question 203031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A mixture of 12 liters of Chemical A, 16 liters of chemical B and 26 liters of chemical C <BR>\n" );
document.write( "is required to kill a destructive crop insect.  Commercial spray X contains 1, 2, and 2 parts, respectively <BR>\n" );
document.write( "of these chemicals.  Commercial spray Y contains only chemical C.  Commercial spray Z contains only <BR>\n" );
document.write( "chemical A and B in equal amounts.  How much of each type of commercial spray is needed to get the <BR>\n" );
document.write( "desired mixture? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153167 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=153167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -----<BR>\n" );
document.write( "product X contains 1 2 2 parts A B C respectively.<BR>\n" );
document.write( "product Y contains 0 0 1 parts A B C respectively.<BR>\n" );
document.write( "product Z contains 1 1 0 parts A B C respectively.<BR>\n" );
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document.write( "you can only buy whole products, so:<BR>\n" );
document.write( "let f = number of product X<BR>\n" );
document.write( "let g = number of product Y<BR>\n" );
document.write( "let h = number of product Z<BR>\n" );
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document.write( "you will want to buy<BR>\n" );
document.write( "f*X + g*Y + h*Z<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "f*X = f*(1A + 2B + 2C)<BR>\n" );
document.write( "g*Y = g*(0A + 0B + 1C)<BR>\n" );
document.write( "h*Z = h*(1A + 1B + 0C)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the total liters of chemical A = 12, then:<BR>\n" );
document.write( "f*1 + g*0 + h*1 = 12 which can be written as 1f + 0g + 1h = 12<BR>\n" );
document.write( "since the total liters of chemical B = 16, then:<BR>\n" );
document.write( "f*2 + g*0 + h*1 = 16 which can be written as 2f + 0g + 1h = 16<BR>\n" );
document.write( "since the total liters of chemical C = 28, then:<BR>\n" );
document.write( "f*2 + g*1 + h*0 = 26 which can be written as 2f + 1g + 0h = 26<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have a series of equations that need to be solved simultaneously to get the same value for f, g, and h in each.<BR>\n" );
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document.write( "the equations are:<BR>\n" );
document.write( "1f + 0g + 1h = 12<BR>\n" );
document.write( "2f + 0g + 1h = 16<BR>\n" );
document.write( "2f + 1g + 0h = 26<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if You subtract the second equation from the first, You get:<BR>\n" );
document.write( "f = 4<BR>\n" );
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document.write( "if You substitute f = 4 in either the first or second equation, You get:<BR>\n" );
document.write( "h = 8<BR>\n" );
document.write( "You will get the same answer using either one.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if You substitute f = 4 in the third equation, You get:<BR>\n" );
document.write( "g = 18<BR>\n" );
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document.write( "your answer should be:<BR>\n" );
document.write( "f = 4<BR>\n" );
document.write( "g = 18<BR>\n" );
document.write( "h = 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "To prove this is true, substitute those values in the following product equation.<BR>\n" );
document.write( "f*X + g*Y + h*Z<BR>\n" );
document.write( "which represents the number of each product you need to buy.<BR>\n" );
document.write( "f*X = 4 * (1A + 2B + 2C) = 4A + 8B + 8C<BR>\n" );
document.write( "g*Y = 18 * (0A + 0B + 1C) = 18C<BR>\n" );
document.write( "h*Z = 8* (1A + 1B + 0C) = 8A + 8B.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the total liters of A is 4 + 8 = 12<BR>\n" );
document.write( "the total liters of B is 8 + 8 = 16<BR>\n" );
document.write( "the total liter of C is 8 + 18 = 26<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the total liters of chemicals A, B, C check out ok, then You need to buy:<BR>\n" );
document.write( "4 packages of product X.<BR>\n" );
document.write( "18 packages of product Y.<BR>\n" );
document.write( "8 packages of product Z.<BR>\n" );
document.write( "under the assumption that the parts of each chemical listed in each product was the liters of each chemical in that product, and not just the ratio, i.e. product Y ratio was 0 0 1 which is interpreted to mean 0 liters of chemical A and 0 liters of chemical B and 1 liter of chemical C are contained in 1 package of product Y for a total of 1 liter.<BR>\n" );
document.write( "Similarly product Z is interpreted to contain 1 liter of chemical A and 1 liter of chemical B for a total of 2 liters.<BR>\n" );
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document.write( " </SPAN>\n" );
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