document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939904>Question 939904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A natural food store makes its own brand of trail mix out of dried apples, raisins, and peanuts. One pound of the mixture costs $3.18. It contains twice as much peanuts by weight as apples. One pound of dried apples cost $4.48, one pound of raisins $2.40, and one pound of peanuts $3.44. How many ounces of each ingredient are contained in one pound of the trail mix?\r<BR>\n" );
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document.write( "I have to use a 3x3 matrix to slove it but I can't figure out what the 3 equations would be </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #572766 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=572766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Do all as pounds and convert to ounces after solution of pounds is found.\r<BR>\n" );
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document.write( "Variables, a, r, p, for apples, raisins, peanuts\r<BR>\n" );
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document.write( "PRICES<BR>\n" );
document.write( "Apples, 4.48<BR>\n" );
document.write( "Raisins, 2.40<BR>\n" );
document.write( "Peanuts, 3.44\r<BR>\n" );
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document.write( "Account for the price of mixture, $3.18/pound.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284.48a%2B2.40r%2B3.44p%29%2F%28a%2Br%2Bp%29=3.18 ALIGN=MIDDLE  ALT=\"%284.48a%2B2.40r%2B3.44p%29%2F%28a%2Br%2Bp%29=3.18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.48a%2B2.40r%2B3.44p=3.18%28a%2Br%2Bp%29 ALIGN=MIDDLE  ALT=\"4.48a%2B2.40r%2B3.44p=3.18%28a%2Br%2Bp%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=448a%2B240r%2B344p=318%28a%2Br%2Bp%29 ALIGN=MIDDLE  ALT=\"448a%2B240r%2B344p=318%28a%2Br%2Bp%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=112a%2B60r%2B86p=79.5%28a%2Br%2Bp%29 ALIGN=MIDDLE  ALT=\"112a%2B60r%2B86p=79.5%28a%2Br%2Bp%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---not like this step<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=224a%2B120r%2B172p=159%28a%2Br%2Bp%29 ALIGN=MIDDLE  ALT=\"224a%2B120r%2B172p=159%28a%2Br%2Bp%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28224-159%29a%2B%28120-159%29r%2B%28172-159%29p=0 ALIGN=MIDDLE  ALT=\"%28224-159%29a%2B%28120-159%29r%2B%28172-159%29p=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2865a-39r%2B13p=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%2865a-39r%2B13p=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, one of the equations for the system.\r<BR>\n" );
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document.write( "Peanuts and Apples relationship:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Fa=2 ALIGN=MIDDLE  ALT=\"p%2Fa=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, meaning <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28p=2a%29 ALIGN=MIDDLE  ALT=\"highlight_green%28p=2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, another equation for the system.\r<BR>\n" );
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document.write( "How much mixture?<BR>\n" );
document.write( "ONE pound.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28a%2Br%2Bp=1%29 ALIGN=MIDDLE  ALT=\"highlight_green%28a%2Br%2Bp=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now you have all the equations for the system.\r<BR>\n" );
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document.write( "Including coefficients of possible 0, or zero, and ordered first three columns as a, r, p, the system can be as this:<BR>\n" );
document.write( "65a-39r+13p=0,2a-p=0,a+r+p=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2865a-39r%2B13p=0%2C2a%2B0%2Ar-p=0%2Ca%2Br%2Bp=1%29 ALIGN=MIDDLE  ALT=\"system%2865a-39r%2B13p=0%2C2a%2B0%2Ar-p=0%2Ca%2Br%2Bp=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That negative sign in the first equation seems unexpected.  I might have made a mistake in the work for that equation.\r<BR>\n" );
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document.write( "You can recheck, and then finish the solution process.\r<BR>\n" );
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document.write( "Notice also, the coefficients of the first equation are products of 13, so<BR>\n" );
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