document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203028>Question 1203028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> By volume, one alloy is 60, copper, 30, zinc, and 10, nickel. A second alloy has percents of 50,<BR>\n" );
document.write( "30, and 20, respectively. A third alloy is 30, copper and 70, nickel. How much of each alloy is<BR>\n" );
document.write( "needed to make 100 cm3 of a resulting alloy with percents of 40, 15, and 45, respectively? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838251 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=838251\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "x = cm^3 of alloy A<BR>\n" );
document.write( "y = cm^3 of alloy B<BR>\n" );
document.write( "z = cm^3 of alloy C<br><BR>\n" );
document.write( "The copper equation: 60% of x, plus 50% of y, plus 30% of z, is equal to 40% of the total 100 cm^3:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.60x%2B.50y%2B.30x=40 ALIGN=MIDDLE  ALT=\".60x%2B.50y%2B.30x=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<br><BR>\n" );
document.write( "The zinc equation: 50% of x, plus 30% of y, and none of z, is equal to 15% of the total 100 cm^3:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.50x%2B.30y=15 ALIGN=MIDDLE  ALT=\".50x%2B.30y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > [2]<br><BR>\n" );
document.write( "The nickel equation: 30% of x, plus 20% of y, plus 70% of z, is equal to 45% of the total 100 cm^3:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.30x%2B.20y%2B.70z=45 ALIGN=MIDDLE  ALT=\".30x%2B.20y%2B.70z=45\"   DISABLED_style= \"max-width:90%; height:auto;\" > [3]<br><BR>\n" );
document.write( "For an algebraic solution, since equation [2] involves only x and y, eliminate z between equations [1] and [3] to get a second equation involving only x and y.  Then that pair of equations can be solved for x and y, leading to a solution of the whole problem.<br><BR>\n" );
document.write( "Multiply [1] by 7 and [3] by 3 and find the difference to eliminate z:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.20x%2B3.50y%2B2.10z=280 ALIGN=MIDDLE  ALT=\"4.20x%2B3.50y%2B2.10z=280\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.90x%2B.60y%2B2.10z=135 ALIGN=MIDDLE  ALT=\".90x%2B.60y%2B2.10z=135\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.30x%2B2.90y=145 ALIGN=MIDDLE  ALT=\"3.30x%2B2.90y=145\"   DISABLED_style= \"max-width:90%; height:auto;\" > [4]<br><BR>\n" );
document.write( "Now solve [2] and [4].<br><BR>\n" );
document.write( "Multiply [2] by 33 and [4] by 5....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16.50x%2B9.90y=495 ALIGN=MIDDLE  ALT=\"16.50x%2B9.90y=495\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16.50x%2B14.50y=725 ALIGN=MIDDLE  ALT=\"16.50x%2B14.50y=725\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.60y=230 ALIGN=MIDDLE  ALT=\"4.60y=230\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=230%2F4.60=50 ALIGN=MIDDLE  ALT=\"y=230%2F4.60=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.50x%2B.30%2850%29=15 ALIGN=MIDDLE  ALT=\".50x%2B.30%2850%29=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.50x%2B15=15 ALIGN=MIDDLE  ALT=\".50x%2B15=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: none of alloy A, and 50 cm^3 each of alloys B and C<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );