document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=831449>Question 831449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> By weight (A) fertilizer is 20%K, 30%N and 50%P, (B) fertilizer is 10, 30, 60 and (C) fertilizer is 0, 40, 60.  How much of each must be mixed to obtain 200lbs of 10%K, 32.5%N, and 57.5%P.\r<BR>\n" );
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document.write( ".20k + .30n + .50p  (A)<BR>\n" );
document.write( ".10k + .30n + .60p  (B)<BR>\n" );
document.write( ".00k + .40n + .60p  (C)\r<BR>\n" );
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document.write( ".10k + 32.5n + .60p = 200 (D)<BR>\n" );
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document.write( "Ak + Bk + Ck = Dk ????? <BR>\n" );
document.write( "An + Bn + Cn = Dn ?????<BR>\n" );
document.write( "Ap + Bp + Cp = Dp ?????\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501416 by </B><A HREF=/tutors/aboutme.mpl?userid=Elomeht><B>Elomeht(22)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Elomeht><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=501416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The important point to note is that the total weight of the mixture is 200.  Start with that.\r<BR>\n" );
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document.write( "Since the desired ratio of K/N/P will be 10%/32.5%/57.5%, we know that the total amounts are:<BR>\n" );
document.write( "K amount = 0.1 times 200 = 20<BR>\n" );
document.write( "N amount = 0.325 times 200 = 65<BR>\n" );
document.write( "P amount = 0.575 times 200 = 115\r<BR>\n" );
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document.write( "Let the amount of each fertilizer be A, B and C respectively.\r<BR>\n" );
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document.write( "Then<BR>\n" );
document.write( "1.  .2A + .1B = 20<BR>\n" );
document.write( "2.  .3A + .3B + .4C = 65<BR>\n" );
document.write( "3.  .5A +.6B + .6C = 115\r<BR>\n" );
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document.write( "From 1, A = 100 - .5B\r<BR>\n" );
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document.write( "From 2, .3(100 - .5B) + .3B + .4C = 65;  30 -.15B + .3B + .4C = 65;<BR>\n" );
document.write( "        B = (35 - .4C)/.15\r<BR>\n" );
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document.write( "So in 3, .5[100 - .5(35 - .4C)/.15] + .6[(35 -.4C)/.15] + .6C = 115;\r<BR>\n" );
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document.write( "50 - .25(35 - .4C)/.15 + 4(35 - .4C) + .6C = 115;<BR>\n" );
document.write( "50 - (8.75 - .1C)/.15 + 140 - 1.6C + .6C = 115;\r<BR>\n" );
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document.write( "7.5 -8.75 + .1C + 21 - .24C + .09C = 17.25<BR>\n" );
document.write( "2.5 = 0.05C\r<BR>\n" );
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document.write( "C = 2.5/0.05 = 50;<BR>\n" );
document.write( "B = [35 - (.4 times 50)]/.15 =  15/.15 = 100<BR>\n" );
document.write( "A = 100 - (.5 times 100) = 100 - 50 = 50<BR>\n" );
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