document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165355>Question 1165355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A metallurgist needs to make 12 grams of an alloy containing 60% gold. He is going to melt and combine one metal that is 90% gold with another metal that is 40% gold. How much of each should he use? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789862 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789862\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "That other tutor loves that formula with all those variables representing the numbers in the problem.<br><BR>\n" );
document.write( "I dislike memorizing formulas with lots of variables that I can derive in a couple of seconds....<br><BR>\n" );
document.write( "A traditional algebraic approach would be something like this:<br><BR>\n" );
document.write( "x grams of 40%, plus (12-x) grams of 90%, equals 12 grams of 60%:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.40%28x%29%2B.90%2812-x%29+=+.60%2812%29 ALIGN=MIDDLE  ALT=\".40%28x%29%2B.90%2812-x%29+=+.60%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The equation is easily solved using basic algebra.<br><BR>\n" );
document.write( "If a formal algebraic solution is not required, here is a much faster path to the answer (for ANY 2-part mixture problem like this).<br><BR>\n" );
document.write( "The target 60% is 2/5 of the way from 40% to 90%.  (Picture the three percentages on a number line, if it helps -- 60 is 20/50 = 2/5 of the way from 40 to 90....)<br><BR>\n" );
document.write( "Therefore, 2/5 of the mixture needs to be the higher percentage metal.<br><BR>\n" );
document.write( "ANSWER: 2/5 of 12 grams, or 4.8 grams, of 90%; the other 7.2 grams of 40%.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( ".90(4.8)+.40(7.2) = 4.32+2.88 = 7.20<BR>\n" );
document.write( ".60(12) = 7.20<br><BR>\n" );
document.write( " </SPAN>\n" );
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