document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154951>Question 1154951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound, how much of each kind of nut should be included in the mixed bag?\r<BR>\n" );
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document.write( "This is my answer: cashews: 0.42 lb.; peanuts: 0.08 1b. \r<BR>\n" );
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document.write( "Is this correct?  Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777468 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=777468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Without doing any detailed calculations, no -- your answer is not right.<br><BR>\n" );
document.write( "Your answer uses far more cashews than peanuts, so the price per pound should be much closer to $5.50 than it is to $2.30.  But $2.80 is much closer to $2.30 than it is to $5.50.<br><BR>\n" );
document.write( "A standard algebraic solution would go something like this....<br><BR>\n" );
document.write( "x = pounds of cashews at $5.50 per pound<BR>\n" );
document.write( "0.5-x = pounds of peanuts at $2.30 per pound<br><BR>\n" );
document.write( "The combined mixture is a half pound worth $2.80 per pound:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%285.5%29%2B%280.5-x%29%282.3%29+=+0.5%282.8%29 ALIGN=MIDDLE  ALT=\"x%285.5%29%2B%280.5-x%29%282.3%29+=+0.5%282.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can finish solving the problem by that method if you want.  It is straightforward; but somewhat ugly, given all the decimals.<br><BR>\n" );
document.write( "Here is a solution using the method I like to use for solving mixture problems like this.<br><BR>\n" );
document.write( "(1) The target price per pound, $2.80, is 5/32 of the way from $2.30 to $5.50.  (Picture the three prices -- 2.30, 2.80, and 5.50 -- on a number line.  From 2.30 to 5.50 is 3.20; from 2.30 to 2.80 is 0.50.  2.80 is 0.50/3.20 = 5/32 of the way from 2.30 to 5.50.)<br><BR>\n" );
document.write( "That means 5/32 of the mixture is the more expensive cashews.<br><BR>\n" );
document.write( "ANSWER: (5/32) of the 1/2 pound mixture -- so 5/64 pounds -- are cashews;  the remaining 27/64 pounds are peanuts.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F64%29%285.50%29%2B%2827%2F64%29%282.30%29+=+1.40 ALIGN=MIDDLE  ALT=\"%285%2F64%29%285.50%29%2B%2827%2F64%29%282.30%29+=+1.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%282.80%29+=+1.40 ALIGN=MIDDLE  ALT=\"%281%2F2%29%282.80%29+=+1.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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