document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=995434>Question 995434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A silversmith wishes to obtain an alloy containing at least 72% silver and at most 75% silver. Determine the greatest and least amounts of an 80% silver alloy that should be combined with a 65% silver alloy in order to have 30grams of the required alloy. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614224 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=614224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is 2 problems in 1<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = grams of 80% alloy needed<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = grams of 65% alloy needed<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "First solve for 72% silver end result<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+b+=+30+ ALIGN=MIDDLE  ALT=\"+a+%2B+b+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+.8a+%2B+.65b+%29+%2F+30+=+.72+ ALIGN=MIDDLE  ALT=\"+%28+.8a+%2B+.65b+%29+%2F+30+=+.72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.8a+%2B+.65b+=+.72%2A30+ ALIGN=MIDDLE  ALT=\"+.8a+%2B+.65b+=+.72%2A30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.8a+%2B+.65b+=+21.6+ ALIGN=MIDDLE  ALT=\"+.8a+%2B+.65b+=+21.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+80a+%2B+65b+=+2160+ ALIGN=MIDDLE  ALT=\"+80a+%2B+65b+=+2160+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16a+%2B+13b+=+432+ ALIGN=MIDDLE  ALT=\"+16a+%2B+13b+=+432+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Multiply both sides of (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13+ ALIGN=MIDDLE  ALT=\"+13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and subtract (1) from (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16a+%2B+13b+=+432+ ALIGN=MIDDLE  ALT=\"+16a+%2B+13b+=+432+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-13a+-+13b+=+-390+ ALIGN=MIDDLE  ALT=\"+-13a+-+13b+=+-390+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3a+=+42+ ALIGN=MIDDLE  ALT=\"+3a+=+42+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+14+ ALIGN=MIDDLE  ALT=\"+a+=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14+%2B+b+=+30+ ALIGN=MIDDLE  ALT=\"+14+%2B+b+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+16+ ALIGN=MIDDLE  ALT=\"+b+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Now solve for 75% alloy end result<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+b+=+30+ ALIGN=MIDDLE  ALT=\"+a+%2B+b+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+.8a+%2B+.65b+%29+%2F+30+=+.72+ ALIGN=MIDDLE  ALT=\"+%28+.8a+%2B+.65b+%29+%2F+30+=+.72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.8a+%2B+.65b+=+.75%2A30+ ALIGN=MIDDLE  ALT=\"+.8a+%2B+.65b+=+.75%2A30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.8a+%2B+.65b+=+22.5+ ALIGN=MIDDLE  ALT=\"+.8a+%2B+.65b+=+22.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+80a+%2B+65b+=+2250+ ALIGN=MIDDLE  ALT=\"+80a+%2B+65b+=+2250+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16a+%2B+13b+=+450+ ALIGN=MIDDLE  ALT=\"+16a+%2B+13b+=+450+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Multiply both sides of (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13+ ALIGN=MIDDLE  ALT=\"+13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and subtract (1) from (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16a+%2B+13b+=+450+ ALIGN=MIDDLE  ALT=\"+16a+%2B+13b+=+450+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-13a+-+13b+=+-390+ ALIGN=MIDDLE  ALT=\"+-13a+-+13b+=+-390+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3a+=+60+ ALIGN=MIDDLE  ALT=\"+3a+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+20+ ALIGN=MIDDLE  ALT=\"+a+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+%2B+b+=+30+ ALIGN=MIDDLE  ALT=\"+20+%2B+b+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+10+ ALIGN=MIDDLE  ALT=\"+b+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "From these results,<BR>\n" );
document.write( "the least amount of 80% alloy needed is 14 grams ( making 72% silver )<BR>\n" );
document.write( "the most amount of 80% alloy needed is 20 grams ( making 75% silver )<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "You can check the answers by plugging<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > back into (2) for both<BR>\n" );
document.write( "72% and 75% cases </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );