document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190205>Question 1190205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bags of coffee worth $90 a bag must be mixed with coffee worth $75 a bag to get 50 bags worth $87 a bag. How many bags of each are needed? </SPAN>\n" );
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document.write( "Let's define two brand labels such that<BR>\n" );
document.write( "Brand A is worth $90 per bag<BR>\n" );
document.write( "Brand B is worth $75 per bag\r<BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "x = number of bags of brand A<BR>\n" );
document.write( "y = number of bags of brand B\r<BR>\n" );
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document.write( "The final mix has 50 bags total, so,<BR>\n" );
document.write( "x+y = 50<BR>\n" );
document.write( "y = 50-x<BR>\n" );
document.write( "which we'll use later in substitution\r<BR>\n" );
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document.write( "90x = total cost of buying x bags of brand A<BR>\n" );
document.write( "75y = total cost of buying y bags of brand B<BR>\n" );
document.write( "90x+75y = total cost buying all bags of coffee\r<BR>\n" );
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document.write( "We divide this total cost by the number of bags overall (50) to get the final cost per bag ($87)\r<BR>\n" );
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document.write( "(total cost)/(total number of bags) = final cost per bag<BR>\n" );
document.write( "(90x+75y)/(50) = 87<BR>\n" );
document.write( "90x+75y = 87*(50)<BR>\n" );
document.write( "90x+75y = 4350\r<BR>\n" );
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document.write( "Now we plug in y = 50-x and solve for x.<BR>\n" );
document.write( "90x+75y = 4350<BR>\n" );
document.write( "90x+75( y ) = 4350<BR>\n" );
document.write( "90x+75( 50-x ) = 4350<BR>\n" );
document.write( "90x+75*50-75x = 4350<BR>\n" );
document.write( "90x+3750-75x = 4350<BR>\n" );
document.write( "15x+3750 = 4350<BR>\n" );
document.write( "15x = 4350-3750<BR>\n" );
document.write( "15x = 600<BR>\n" );
document.write( "x = 600/15<BR>\n" );
document.write( "<font color=red>x = 40</font>\r<BR>\n" );
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document.write( "Then compute the value of y<BR>\n" );
document.write( "y = 50-x<BR>\n" );
document.write( "y = 50-40<BR>\n" );
document.write( "<font color=blue>y = 10</font>\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "<font color=red>40 bags</font> of the $90 per bag brand.<BR>\n" );
document.write( "<font color=blue>10 bags</font> of the $75 per bag brand.<BR>\n" );
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