document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534086>Question 534086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A silversmith has two alloys, one containing 70% silver and the other 20% silver. How much of each should be melted and combined to obtain 500 grams of an alloy containing 55% silver? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351311 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=351311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the amount (in grams) of the 70% alloy.<BR>\n" );
document.write( "Let y be the amount (in grams) of the 20% alloy.<BR>\n" );
document.write( "We want<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=500 ALIGN=MIDDLE  ALT=\"x%2By=500\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.7x%2B0.2y=0.55%2A500 ALIGN=MIDDLE  ALT=\"0.7x%2B0.2y=0.55%2A500\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.7x%2B0.2y=275 ALIGN=MIDDLE  ALT=\"0.7x%2B0.2y=275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have a system of linear equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=500 ALIGN=MIDDLE  ALT=\"x%2By=500\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.7x%2B0.2y=275 ALIGN=MIDDLE  ALT=\"0.7x%2B0.2y=275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can solve by elimination like this:<BR>\n" );
document.write( "multiply the first equation times -0.2 to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.2x-0.2y=-100 ALIGN=MIDDLE  ALT=\"-0.2x-0.2y=-100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and add it to the second equation to eliminate y, getting<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5x=175 ALIGN=MIDDLE  ALT=\"0.5x=175\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=175%2F0.5=340 ALIGN=MIDDLE  ALT=\"x=175%2F0.5=340\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plugging that value back into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=500 ALIGN=MIDDLE  ALT=\"x%2By=500\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=340%2By=500 ALIGN=MIDDLE  ALT=\"340%2By=500\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=500-340=150 ALIGN=MIDDLE  ALT=\"y=500-340=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );