document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=951263>Question 951263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> By weight, one fertilizer is 10% potassium, 40% nitrogen, and 50% phosphorus. A second fertilizer has percents of 10, 30, 60, respectively, and a third has percents of 0, 20, 80, respectively. How much of each must be mixed to get 200 pounds with 8, 31, 61 percent? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580878 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=580878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By weight, one fertilizer is 10% potassium, 40% nitrogen, and 50% phosphorus.<BR>\n" );
document.write( " A second fertilizer has percents of 10, 30, 60, respectively, <BR>\n" );
document.write( " and a third has percents of 0, 20, 80, respectively.<BR>\n" );
document.write( " How much of each must be mixed to get 200 pounds with 8, 31, 61 percent?<BR>\n" );
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document.write( "let a = amt of 1st fertilizer<BR>\n" );
document.write( "let b = amt of 2nd fertilizer<BR>\n" );
document.write( "let c = amt of third fertilizer<BR>\n" );
document.write( "we know<BR>\n" );
document.write( "a + b + c = 200; the total amt equation<BR>\n" );
document.write( "and<BR>\n" );
document.write( "Write an equation for each substance using decimals for percent<BR>\n" );
document.write( ".10a + .10b + 0c = .08(200); potassium<BR>\n" );
document.write( ".40a + .30b + .20c= .31(200); nitrogen<BR>\n" );
document.write( ".50a + .60b + .80c = .61(200); phosphorus<BR>\n" );
document.write( ":<BR>\n" );
document.write( ".10a + .10b + 0c = 16<BR>\n" );
document.write( ".40a + .30b + .20c = 62<BR>\n" );
document.write( ".50a + .60b + .80c = 122<BR>\n" );
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document.write( "Multiply the 1st substance equation by 10, subtract from the total amt equation<BR>\n" );
document.write( "a + b + c = 200<BR>\n" );
document.write( "a + b + 0 = 160<BR>\n" );
document.write( "-----------------Subtraction eliminate a and b, find c<BR>\n" );
document.write( "0 + 0 + c = 40 lb of phosphorus<BR>\n" );
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document.write( "using the 2nd and 3rs substance equations, replace c with 40<BR>\n" );
document.write( ".40a + .30b + .20(40) = 62<BR>\n" );
document.write( ".50a + .60b + .80(40) = 122<BR>\n" );
document.write( ":<BR>\n" );
document.write( ".40a + .30b + 8 = 62<BR>\n" );
document.write( ".50a + .60b + 32 = 122<BR>\n" );
document.write( ":<BR>\n" );
document.write( ".40a + .30b = 54<BR>\n" );
document.write( ".50a + .60b = 90<BR>\n" );
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document.write( "multiply the 1st \"two unknown\" equation by 2 subtract the 2nd<BR>\n" );
document.write( ".80a + .60b = 108<BR>\n" );
document.write( ".50a + .60b = 90<BR>\n" );
document.write( "--------------------subtraction eliminates b find a<BR>\n" );
document.write( ".30a + 0 = 18<BR>\n" );
document.write( "a = 18/.3<BR>\n" );
document.write( "a = 60 lb of potassium<BR>\n" );
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document.write( "Find b (nitrogen)<BR>\n" );
document.write( "200 - 40 - 60 = 100 lb of nitrogen <BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"How much of each must be mixed to get 200 pounds with 8, 31, 61 percent?<BR>\n" );
document.write( "60, 100, 40<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can check this for yourself in one of the substance equations<BR>\n" );
document.write( ".50(60) + .60(100) + .80(40) = .61(200); phosphorus<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );