document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=245917>Question 245917</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A store mixes Kenyan coffee worth $10 per kilogram and Venezuelan coffee worth $12 per kilogram.  The mixture is to sell for $11 per kilogram.  Find how much of each should be used to make a 360-kilogram mixture<BR>\n" );
document.write( "How many kilograms of the Kenyan coffee should be in the mixture? _____ Kg </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179631 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=179631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can start this problem thinking in terms of<BR>\n" );
document.write( "K amount of Kenyan coffee @ $10 per kilogram<BR>\n" );
document.write( "+ V amount of Venezuelan coffee @ $12 per kilogram<BR>\n" );
document.write( "= 360 kg @ $11/kg<BR>\n" );
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document.write( "The problem asks how many kg of Kenyan coffee in the mixture.<BR>\n" );
document.write( "Well, it can be said the amount is 360 - V.  <BR>\n" );
document.write( "That is, the amount of Kenyan = known total - unknown amount of Venezuelan coffee.<BR>\n" );
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document.write( "At first, this may not seem like much help. But in fact, that is one of the key ways to reduce the number of unknown variables in algebra word problems.<BR>\n" );
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document.write( "K = 360 - V<BR>\n" );
document.write( "V = V<BR>\n" );
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document.write( "Substituting in the total cost equation:<BR>\n" );
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document.write( "10*(360-V) + 12*(V) = 360*11<BR>\n" );
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document.write( "Multiplying through:<BR>\n" );
document.write( "3600-10V + 12V = 3960<BR>\n" );
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document.write( "Collecting like terms<BR>\n" );
document.write( "3600 + 2V = 3960<BR>\n" );
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document.write( "Subtracting 3600 from both sides<BR>\n" );
document.write( "2V = 360<BR>\n" );
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document.write( "Dividing both sides by 2<BR>\n" );
document.write( "V = 180<BR>\n" );
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document.write( "So, V  = 180, which means K = 360-180 = 180.<BR>\n" );
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document.write( "We have equal amount of K and V in the total, which makes sense because we want the mixture to cost $11/kg and the two components cost $10/kg and $12/kg.  $11/kg is the average.<BR>\n" );
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document.write( "We can check our work by substitution back into the equation to see if our result produces the given result.<BR>\n" );
document.write( "180*10 + 180*12 = 36*11<BR>\n" );
document.write( "1800 + 2160 = 3960 = 36*11<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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