document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=111614>Question 111614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A goldsmith has two alloys that are different purities of gold. The first is three-fourths pure gold and the second is five-twelths pure gold. How many ounces of each should be melted and mixed in order to obtain a 6-oz mixture that is two-thirds pure gold? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81478 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=81478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let x=amount of 3/4 pure gold needed\r<BR>\n" );
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document.write( "Then 6-x=amount of 5/12 pure gold needed\r<BR>\n" );
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document.write( "Now we know that the amount of pure gold in the 3/4 alloy ((3/4)x) plus the amount of pure gold in the 5/12 alloy ((5/12)(6-x)) has to equal the amount of pure gold in the final alloy(6*(2/3)).  So our equation to solve is:\r<BR>\n" );
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document.write( "(3/4)x+(5/12)(6-x)=6*(2/3)  simplify\r<BR>\n" );
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document.write( "(3/4)x+(5/2)-(5/12)x=4  multiply each term by 12 (LCM)\r<BR>\n" );
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document.write( "9x+30-5x=48  subtract 30 from both sides<BR>\n" );
document.write( "9x-5x+30-30=48-30  collect like terms\r<BR>\n" );
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document.write( "4x=18  divide both sides by 4\r<BR>\n" );
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document.write( "x=4.5 oz----------------------amount of 3/4 pure gold needed\r<BR>\n" );
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document.write( "6-x=6-4.5=1.5 oz-----------------------amount of 5/12 pure gold needed\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "(4.5)(3/4)+(1.5)(5/12)=6(2/3)\r<BR>\n" );
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document.write( "3.375+0.625=4<BR>\n" );
document.write( "4=4\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
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