document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163847>Question 163847</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Coffee Counter charges $9.00 per pound for Kenyan French Roast coffee and $8.00 per pound for Sumatran coffee. How much of each type should be used to make a 20-lb blend that sells for $8.40 per pound? </SPAN>\n" );
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document.write( "First start by using the formula of Cost = Amount*Price<BR>\n" );
document.write( "We will also need the idea that the amount of Kenyan + the amount of Sumatran will equal the total amount of the mix.\r<BR>\n" );
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document.write( "So setting up our mixture problem we get Cost of Kenyan + Cost of Sumatran = Cost of Mix.\r<BR>\n" );
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document.write( "Now let's set up some variables. Let x be the number of pounds of Kenyan coffee and y be the number of pounds of Sumatran coffee.\r<BR>\n" );
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document.write( "Then x + y = 20 because we are trying to make 20 pounds of the mix.\r<BR>\n" );
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document.write( "So using our Cost formula\r<BR>\n" );
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document.write( "9.00x + 8.00y = 8.40*20 since we have x-lb at $9.00 per lb and y-lb at $8.00 per lb to make a total of 20 lb at $8.40 per lb.\r<BR>\n" );
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document.write( "since x + y = 20 lets solve for y.<BR>\n" );
document.write( "by subtracting y from both sides we get y = 20 - x.\r<BR>\n" );
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document.write( "substituting 20 - x for y in our cost equation we get <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.00x+%2B+8.00%2820-x%29=+8.40%2A20 ALIGN=MIDDLE  ALT=\"9.00x+%2B+8.00%2820-x%29=+8.40%2A20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the distributive property we get<BR>\n" );
document.write( "9.00x + 160 - 8.00x = 168<BR>\n" );
document.write( "simplifying we get<BR>\n" );
document.write( "1.00x + 160 = 168<BR>\n" );
document.write( "solving for x gives us x = 8<BR>\n" );
document.write( "therefore we need 8 lb of the kenyan coffee.<BR>\n" );
document.write( "now we still need the amount of Sumatran so we take 8 + y = 20<BR>\n" );
document.write( "and solve for y to get 12 lb of Sumatran coffee. <BR>\n" );
document.write( "So all together we need 8 lb of Kenyan French Coffee costing $9.00 per pound and  12 lb of Sumatran Coffee costing $8.00 per pound to make 20 lb of a mix costing $8.40 per pound.  </SPAN>\n" );
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