document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=713915>Question 713915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cheese manufacturer combines Romano cheese that costs $4.00 per pound with aged Parmesan cheese which costs $7.00 per pound to make 30 lbs of a grated cheese mixture. How many pounds of each cheese should they include if they want the 30 ound mixture to cost $5.70 per pound? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #438615 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=438615\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The manufacturer wants to mix some high strength cheese with so low strength cheese and have a known quantity of mixture of a known intermediate strength cheese.  Strength here is money, price (some expected dollars per pound).\r<BR>\n" );
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document.write( "M=pounds of mixture, 30 pounds.<BR>\n" );
document.write( "u= amount of low strength, unknown pounds<BR>\n" );
document.write( "v= amount of high strength cheese, unknown pounds<BR>\n" );
document.write( "L = strength of the low strength cheese, $4/pound<BR>\n" );
document.write( "H = high strength cheese, $7/pound<BR>\n" );
document.write( "T = Target price per pound 5.70\r<BR>\n" );
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document.write( "Setup Equations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28Lu%2BHv%29%2FM=T ALIGN=MIDDLE  ALT=\"%28Lu%2BHv%29%2FM=T\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2Bv=M ALIGN=MIDDLE  ALT=\"u%2Bv=M\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve for u and v.<BR>\n" );
document.write( "Sometimes the values given are conveniently chosen to make the solving easy, but you don't want to always rely on that.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Lu%2BHv=TM ALIGN=MIDDLE  ALT=\"Lu%2BHv=TM\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2Bv=M ALIGN=MIDDLE  ALT=\"u%2Bv=M\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "How neat those numbers will be, we not know (unless we substitute them NOW).<BR>\n" );
document.write( "v=M-u, so keep going in symbols, subsituting this one into the percents equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Lu%2BH%28M-u%29=TM ALIGN=MIDDLE  ALT=\"Lu%2BH%28M-u%29=TM\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Lu%2BHM-Hu=TM ALIGN=MIDDLE  ALT=\"Lu%2BHM-Hu=TM\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L-H%29u%2BHM=TM ALIGN=MIDDLE  ALT=\"%28L-H%29u%2BHM=TM\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L-H%29u=TM-HM ALIGN=MIDDLE  ALT=\"%28L-H%29u=TM-HM\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L-H%29u=M%28T-H%29 ALIGN=MIDDLE  ALT=\"%28L-H%29u=M%28T-H%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=M%28T-H%29%2F%28L-H%29 ALIGN=MIDDLE  ALT=\"u=M%28T-H%29%2F%28L-H%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Might be most convenient if done symbolically to use <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28u=M%28H-T%29%2F%28H-L%29%29 ALIGN=MIDDLE  ALT=\"highlight%28u=M%28H-T%29%2F%28H-L%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which was multiplied by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28v=M-u%29 ALIGN=MIDDLE  ALT=\"highlight%28v=M-u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since you just found u.\r<BR>\n" );
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document.write( "Substitute Values to determine values of u and v.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=%28M%287-5.7%29%29%2F%287-4%29 ALIGN=MIDDLE  ALT=\"u=%28M%287-5.7%29%29%2F%287-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which you compute and then find the value for v. </SPAN>\n" );
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