document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105670>Question 105670</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780132404228/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A coffee wholesaler blends together three types of coffee that sell for $2.20, $2.30, and $2.60 per pound, so as to obtain 100 lb of coffee worth $2.40 per pound. If the wholesaler uses the same amount of the two higher priced coffees, how much of each type must be used in the blend? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76906 by </B><A HREF=/tutors/aboutme.mpl?userid=fmo><B>fmo(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fmo><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=76906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let a represent the quantity of the $2.20 type of coffee.<BR>\n" );
document.write( "Let b represent the quantity of the $2.30 type of coffee.<BR>\n" );
document.write( "Let c represent the quantity of the $2.60 type of coffee.\r<BR>\n" );
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document.write( "From the problem we know that the wholesaler is making 100 lbs of coffee, so:<BR>\n" );
document.write( "a + b + c = 100\r<BR>\n" );
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document.write( "We also know that he's using the same amount of the $2.30 type as of the $2.60 type, or b = c.  That being the case we can substitute b in for c in the above equation and we get:<BR>\n" );
document.write( "a + b + b = 100\r<BR>\n" );
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document.write( "Then by combining like terms:<BR>\n" );
document.write( "a + 2b = 100\r<BR>\n" );
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document.write( "We also know from the problem that by mixing these coffee types, the wholesaler arrives at a price of $2.40 per pound of the blend.  He's making 100 lbs, so:<BR>\n" );
document.write( "2.40 * 100 = 240<BR>\n" );
document.write( "is the amount of money used to make the blend.  The cost of each type of coffee used then, would be its price per pound multiplied by the quantity used or:\r<BR>\n" );
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document.write( "2.20a + 2.30b + 2.60b = 240<BR>\n" );
document.write( "2.20a + 4.90b = 240 (after adding the like terms)\r<BR>\n" );
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document.write( "Again, we didn't write 2.60c because the quantity of types b and c are equal.  Now we have a system of equations that we can use to eliminate one of the variables:\r<BR>\n" );
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document.write( "2.20a + 4.90b = 240   eq1<BR>\n" );
document.write( "    a +    2b = 100   eq2\r<BR>\n" );
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document.write( "Multiplying eq1 by 2.20 so that we can eliminate variable a:\r<BR>\n" );
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document.write( "2.20a + 4.90b = 240   eq1<BR>\n" );
document.write( "2.20a + 4.40b = 220   eq2*2.20\r<BR>\n" );
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document.write( "Subtracting eq2*2.20 from eq1 we get:\r<BR>\n" );
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document.write( "0.50b = 20<BR>\n" );
document.write( "b = 10 (after multiplying both sides of the equation by 0.50)\r<BR>\n" );
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document.write( "Substituting b = 10 back into the original equation eq2:\r<BR>\n" );
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document.write( "a + 2(10) = 100<BR>\n" );
document.write( "   a + 20 = 100<BR>\n" );
document.write( "        a = 80\r<BR>\n" );
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document.write( "Therefore, the wholesaler used 80 lbs of the $2.20 coffee, 10 lbs of $2.30 coffee, and 10 lbs of the $2.60 coffee. </SPAN>\n" );
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