document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=332549>Question 332549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18-pound mixture cost $39. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $48. Find the cost per pound of the cinnamon tea and of the spice tea. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238308 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18-pound mixture cost $39. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $48. Find the cost per pound of the cinnamon tea and of the spice tea.<BR>\n" );
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document.write( "Let x = cost per lb of cinnamon tea<BR>\n" );
document.write( "and y = cost per lb of spice tea<BR>\n" );
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document.write( "From:\"A merchant mixed 12 lb of a cinnamon tea with 6 lb of spice tea. The 18-pound mixture cost $39.\" we get equation 1:<BR>\n" );
document.write( "12x + 6y = 39<BR>\n" );
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document.write( "From:\"A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $48.\" we get equation 2:<BR>\n" );
document.write( "14x + 8y = 48<BR>\n" );
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document.write( "Our system of equation is then:<BR>\n" );
document.write( "12x + 6y = 39<BR>\n" );
document.write( "14x + 8y = 48<BR>\n" );
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document.write( "Multiplying top equation by 8 we get:<BR>\n" );
document.write( "96x + 48y = 312<BR>\n" );
document.write( "14x + 8y = 48<BR>\n" );
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document.write( "Mutiplying bottom equation by -6 we get:<BR>\n" );
document.write( " 96x + 48y = 312<BR>\n" );
document.write( "-84x - 48y = -288<BR>\n" );
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document.write( "ADD the two equations together:<BR>\n" );
document.write( " 96x + 48y = 312<BR>\n" );
document.write( "-84x - 48y = -288<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "12x   = 24<BR>\n" );
document.write( "x = $2 per pound (cinnamon tea)<BR>\n" );
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document.write( "Substitute the above into either of the two original equations to find y:<BR>\n" );
document.write( "12x + 6y = 39<BR>\n" );
document.write( "12(2) + 6y = 39<BR>\n" );
document.write( "24 + 6y = 39<BR>\n" );
document.write( "6y = 15<BR>\n" );
document.write( "y = 15/6<BR>\n" );
document.write( "y = $2.50 per pound (spice tea)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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