document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208211>Question 208211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SOLVE USING DETERMINANTS and CRAMER'S RULE\r<BR>\n" );
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document.write( "Three kilos of homegrown tobacco and 8 kilos of imported tobacco cost $39.70 ,and 5 kilos of homegrown tobacco and 6 kilos of imported tobacco cost $47.10. What is the cost per kilo for both kinds of tobacco? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157514 by </B><A HREF=/tutors/aboutme.mpl?userid=pjalgeb><B>pjalgeb(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=pjalgeb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157514\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> REQUIRED: Find y(price of homegrown tobacco) and x(price of imported tobacco)\r<BR>\n" );
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document.write( "SOLUTION:\r<BR>\n" );
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document.write( "              Amount HGT       Amount of IMPT     IMPT Price     HGT Price   Total Price<BR>\n" );
document.write( "              (kilos)          (kilos)            ($ per kilo)  ($ per kilo) ($)\r<BR>\n" );
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document.write( "First Order  |       3        :        8         :     x       :     y      : 3x+8y = 39.7  |\r<BR>\n" );
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document.write( "Second Order |       5        :        6         :     x       :     y      : 5x+6y = 47.1  |<BR>\n" );
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document.write( "The following Equations can be derived from the total price column:\r<BR>\n" );
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document.write( "                 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B8y+=+39.7+ ALIGN=MIDDLE  ALT=\"3x%2B8y+=+39.7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> Equation 1 and \r<BR>\n" );
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document.write( "                 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6y+=+47.1+ ALIGN=MIDDLE  ALT=\"5x%2B6y+=+47.1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> Equation 2<BR>\n" );
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document.write( "Now we have two equations with two unknowns:\r<BR>\n" );
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document.write( "                 3x+8y = 39.7  --> Equation 1<BR>\n" );
document.write( "                 5x+6y = 47.1  --> Equation 2\r<BR>\n" );
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document.write( "The augmented 2x2 matrix for the above system of equations is:\r<BR>\n" );
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document.write( "                | 3  8 | 39.7 |<BR>\n" );
document.write( "                | 5  6 | 47.1 |\r<BR>\n" );
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document.write( "Using Cramer's Rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+Dx%2FD ALIGN=MIDDLE  ALT=\"x+=+Dx%2FD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+Dy%2FD ALIGN=MIDDLE  ALT=\"y+=+Dy%2FD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First we solve for D, Dx and Dy:\r<BR>\n" );
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document.write( "D  = | 3   8 | = 3(6) - 8(5)  = 18 - 40  = - 22 <BR>\n" );
document.write( "     | 5   6 |\r<BR>\n" );
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document.write( "since D is not 0 then we can proceed:\r<BR>\n" );
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document.write( "Dx = | 39.7  8 | = 39.7(6) -8(47.1) = 238.2 - 376.8 = -138.6<BR>\n" );
document.write( "     | 47.1  6 | \r<BR>\n" );
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document.write( "Dy = | 3  39.7 | = 3(47.1) - 5(39.7) = 141.3 - 198.5  = -57.2<BR>\n" );
document.write( "     | 5  47.1 | \r<BR>\n" );
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document.write( "Now we can solve for x and y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+Dx%2FD+=+-138.6%2F-22++=+6.3+ ALIGN=MIDDLE  ALT=\"x+=+Dx%2FD+=+-138.6%2F-22++=+6.3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+Dy%2FD+=+-57.2%2F-22+++=+2.6+ ALIGN=MIDDLE  ALT=\"y+=+Dy%2FD+=+-57.2%2F-22+++=+2.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ANSWER:\r<BR>\n" );
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document.write( "Homegrown tobacco costs $2.60 per kilo while the imported ones costs $6.30 per kilo.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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