document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1145000>Question 1145000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve using substitution/Addition  \r<BR>\n" );
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document.write( "By weight a 10-10-10 fertilizer contains 10.0% nitrogen, 10.0% phosphorus, and 10.0% potash. A 12-0-6<BR>\n" );
document.write( "fertilizer contains 12.0% nitrogen, no phosphorous, and 6.00% potash. A landscaper has three types of<BR>\n" );
document.write( "fertilizer in stock. One is 10-12-15, a second is 10-0-5, and a third is 30-6-15. How much of each must<BR>\n" );
document.write( "be mixed in order to get 400̃ lb of fertilizer that is 16-3-9? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #766183 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=766183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your simultaneous equations to solve become:\r<BR>\n" );
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document.write( ".10x + .10y + .30z = 64<BR>\n" );
document.write( ".12x + 0y + .06z = 12<BR>\n" );
document.write( ".15x + .05y + .15z = 36\r<BR>\n" );
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document.write( "the first equation tells you the total number of pounds of nitrogen you want.<BR>\n" );
document.write( "the second equation tells you the total number of pounds of phosphorus you want.<BR>\n" );
document.write( "the third equation tells you the total number of pounds of potash you want.\r<BR>\n" );
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document.write( "these are all based on the total number of pounds of fertilizer being equal to 400 pounds.\r<BR>\n" );
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document.write( "x is the number of pounds of fertilizer that is 10-12-15.<BR>\n" );
document.write( "y is the number of pounds of fertilizer that is 10-0-5.<BR>\n" );
document.write( "z is the number of pounds of fertilizer that is 30-6-15.\r<BR>\n" );
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document.write( "the total number of pounds of fertilizer that you want is 400.<BR>\n" );
document.write( "that is composed of 16% nitrogen = 64 pounds of nitrogen.<BR>\n" );
document.write( "that is composed of 3% phosphorus = 12 pounds of phosphorus.<BR>\n" );
document.write( "that is composed of 9% potash= 36 pounds of potash.\r<BR>\n" );
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document.write( "the 3 equations you want to solve simultaneously are:\r<BR>\n" );
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document.write( ".10x + .10y + .30z = 64<BR>\n" );
document.write( ".12x + 0y + .06z = 12<BR>\n" );
document.write( ".15x + .05y + .15z = 36\r<BR>\n" );
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document.write( "take the first 2 equations and eliminate the x variable by multiplying both sides of the first equation by 1.2 and then subtracting the second equation from the first to get:<BR>\n" );
document.write( ".12y + .30z = 64.8\r<BR>\n" );
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document.write( "take the second 2 equations and eliminate the x variable by multiplying both sides of second equation by 1.25 and then subtracting the second equation from the third to get:<BR>\n" );
document.write( ".05y + .075z = 21\r<BR>\n" );
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document.write( "you now have two equations in y and z.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( ".12y + .30z = 64.8<BR>\n" );
document.write( ".05y + .075z = 21\r<BR>\n" );
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document.write( "eliminate y by multiplying both sides of the second equation by 2.4 and leaving the first equation as is to get:\r<BR>\n" );
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document.write( ".12y + .30z = 64.8<BR>\n" );
document.write( ".12y + .18z = 50.4\r<BR>\n" );
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document.write( "subtract the second equation from the first to ge:\r<BR>\n" );
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document.write( ".12z = 14.4<BR>\n" );
document.write( "solve for z to get:<BR>\n" );
document.write( "z = 14.4 /.12 = 120\r<BR>\n" );
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document.write( "replace z in the second equation to get:<BR>\n" );
document.write( ".12y + .30z = 64.8 becomes:<BR>\n" );
document.write( ".12y + .30 * 120 = 64.8 which becomes:<BR>\n" );
document.write( ".12y + 36 = 64.8<BR>\n" );
document.write( "subtract 36 from both sides of this equation to get:<BR>\n" );
document.write( ".12y = 28.8<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 28.8 / .12 = 240\r<BR>\n" );
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document.write( "you now have:<BR>\n" );
document.write( "z = 120<BR>\n" );
document.write( "y = 240\r<BR>\n" );
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document.write( "go back to the first original equation and replace z with 120 and y with 240 to get:L<BR>\n" );
document.write( ".10x + .10y + .30z = 64 becomes:<BR>\n" );
document.write( ".10x + .10 * 240 + .30 * 120 = 64 which becomes:<BR>\n" );
document.write( ".10x + 24 + 36 = 64<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( ".10x + 60 = 64<BR>\n" );
document.write( "subtract 60 from both sides of this equation to get:<BR>\n" );
document.write( ".10x = 4<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 4 / .10 = 40\r<BR>\n" );
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document.write( "your solution is that:<BR>\n" );
document.write( "x = 40<BR>\n" );
document.write( "y = 240<BR>\n" );
document.write( "z = 120\r<BR>\n" );
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document.write( "you will need:\r<BR>\n" );
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document.write( "40 pounds of fertilizer that is 10-12-15.<BR>\n" );
document.write( "240 pounds of fertilizer that is 10-0-5.<BR>\n" );
document.write( "120 pounds of fertilizer that is 30-6-15.\r<BR>\n" );
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document.write( "total pounds of fertilizer is equal to 40 + 240 + 120 = 400<BR>\n" );
document.write( "total pounds of nitrogen is .10 * 40 + .10 * 240 + .30 * 120 = 64<BR>\n" );
document.write( "total pounds of phosphorus is .12 * 40 + 0 * 240 + .06 * 120 = 12<BR>\n" );
document.write( "total pounds of potash is .15 * 40 + .05 * 240 + .15 * 120 = 36\r<BR>\n" );
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document.write( " </SPAN>\n" );
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