document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534007>Question 534007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A metal smith wishes to create an alloy of 20%,silverand12% gold. She has three raw materials to work with. One is 10%,silverand10% gold the second is 25%,silverand10% gold, and the final metal is 30%,silverand15% gold. In what proportions should she combine the three to produce the desired alloy?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351476 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=351476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A metal smith wishes to create an alloy of 20% silver and 12% gold. <BR>\n" );
document.write( " One is 10% silver and 10% gold the second is 25% silver and 10% gold, and the final metal is 30% silver and 15% gold. <BR>\n" );
document.write( "In what proportions should he combine the three to produce the desired alloy?<BR>\n" );
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document.write( "Let a = amt of 1st alloy<BR>\n" );
document.write( "let b = amt of 2nd<BR>\n" );
document.write( "let c = amt of 3rd<BR>\n" );
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document.write( "Let's assign a value to the resulting amt. 120 units is good value<BR>\n" );
document.write( "Obviously besides gold and silver, a percentage of filler is in each alloy<BR>\n" );
document.write( "The remaining amt when you subtract the silver and gold.<BR>\n" );
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document.write( "Write an equation for each substance<BR>\n" );
document.write( "Silver: <BR>\n" );
document.write( ".10a + .25b + .30c = .20(120)<BR>\n" );
document.write( ".10a + .25b + .30c = 24<BR>\n" );
document.write( "Gold:<BR>\n" );
document.write( ".10a + .10b + .15c = .12(120) <BR>\n" );
document.write( ".10a + .10b + .15c = 14.4<BR>\n" );
document.write( "Filler:<BR>\n" );
document.write( ".80a + .65b + .55c = .68(120)<BR>\n" );
document.write( ".80a + .65b + .55c = 81.6<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Subtract the 2nd equation from the 1st<BR>\n" );
document.write( ".10a + .25b + .30c = 24<BR>\n" );
document.write( ".10a + .10b + .15c = 14.4<BR>\n" );
document.write( "----------------------------subtraction eliminates a<BR>\n" );
document.write( ".15b + .15c = 9.6<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply the 2nd equation by 8, subtract the 3rd equation<BR>\n" );
document.write( ".80a + .80b + 1.2c = 115.2<BR>\n" );
document.write( ".80a + .65b + .55c = 81.6<BR>\n" );
document.write( "-----------------------------subtraction eliminates a<BR>\n" );
document.write( ".15b + .65c = 33.6<BR>\n" );
document.write( ".15b + .15c = 9.6<BR>\n" );
document.write( "------------------Subtraction eliminates b, find c<BR>\n" );
document.write( ".50c = 24<BR>\n" );
document.write( "c = 48 units of the 3rd alloy<BR>\n" );
document.write( "Find b<BR>\n" );
document.write( ".15b + .15(48) = 9.6<BR>\n" );
document.write( ".15b = 9.6 - 7.2<BR>\n" );
document.write( ".15b = 2.4<BR>\n" );
document.write( "b = 2.4/.15.10a + .25b + .30c = 24<BR>\n" );
document.write( "b = 16 units of the 2nd alloy<BR>\n" );
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document.write( "Find a<BR>\n" );
document.write( ".10a + .25b + .30c = 24<BR>\n" );
document.write( ".10a + .25(16) + .30(48) = 24<BR>\n" );
document.write( ".10a + 4 + 14.4 = 24<BR>\n" );
document.write( ".10a = 24 - 18.4<BR>\n" );
document.write( ".10a = 5.6<BR>\n" );
document.write( "a = 56 units of the 1st alloy<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a:b:c<BR>\n" );
document.write( "56:16:48<BR>\n" );
document.write( "reduce using 8 as a divisor<BR>\n" );
document.write( "7:2:6 is the proportion of the 3 alloys<BR>\n" );
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document.write( "I'll let you confirm that the math is correct here\r<BR>\n" );
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document.write( " </SPAN>\n" );
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