document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346583>Question 346583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The amounts (by weight) of gold, silver, and lead in three alloys of these metals are in the ratio 4:3:2 in the first alloy, 3:5:1 in the second, and 2:2:5 in the third. It is desired to make an alloy containing equal amounts (by weight) of gold, silver, and lead. How many ounces of each alloy should be used for every 10 ounces of the new mixture?\r<BR>\n" );
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document.write( "thanks........ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247816 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=247816\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given<BR>\n" );
document.write( "three alloys;  A1,A2,A3<BR>\n" );
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document.write( "weight equation 1: A1+A2+A3=10<BR>\n" );
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document.write( "make up of each alloy: Gold, silve and lead ratio 4:3:2 in the first alloy, 3:5:1 in the second, and 2:2:5 in the third<BR>\n" );
document.write( "want: It is desired to make an alloy containing equal amounts (by weight) of gold, silver, and lead<BR>\n" );
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document.write( "Gold:  4/9*A1+3/9*A2+2/9*A3=10*1/3<BR>\n" );
document.write( "silver: 3/9*A1+5/9*A2+2/9*A3=10*1/3<BR>\n" );
document.write( "lead: 2/9*A1+1/9*A2+5/9*A3=10*1/3<BR>\n" );
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document.write( "multiply the gold, silver and lead equations by 9 to eliminate fractions<BR>\n" );
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document.write( "Gold equation 2: 4A1+3A2+2A3=30<BR>\n" );
document.write( "Silver equation 3: 3A1+5A2+2A3=30<BR>\n" );
document.write( "lead equation 4: 2A1+A2+5A3=30<BR>\n" );
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document.write( "subtract equation 3 from equ 2:  A1-2A2=0 or A1=2A2<BR>\n" );
document.write( "mult eq 3 by 5  15A1+25A2+10A3=150<BR>\n" );
document.write( "mult eq 4 by -2  -4A1-2A2-10A3=-60<BR>\n" );
document.write( "add these equtions  11A1+23A2=90<BR>\n" );
document.write( "substitute A1=2A2 into above equation<BR>\n" );
document.write( "22A2+23A2=90 ---> 45A2=90 or  A2=2<BR>\n" );
document.write( "since A1=2A2=4<BR>\n" );
document.write( "since A1+A2+A3=10 then A3=4<BR>\n" );
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document.write( "Validate answers by taking the original equaitons substituting these values<BR>\n" );
document.write( "ie lead: 2/9*A1+1/9*A2+5/9*A3=10*1/3<BR>\n" );
document.write( "lead: 2/9*4+1/9*2+5/9*4=10*1/3<BR>\n" );
document.write( "8/9+2/9+20/9=10/3<BR>\n" );
document.write( "30/9=10/3 checks\r<BR>\n" );
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