document.write( "Question 107122: Your company offers gourmet coffee beans for $14 per pound and regular coffee beans for $6 per pound. If I put 12 pounds of the gourmet coffee beans in the mixer, how much of the regular coffee beans do I add to get a mixture that costs $8 per pound? \n" ); document.write( "
Algebra.Com's Answer #78062 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Here's one way of looking at this problem.
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\n" ); document.write( "Let's start with the understanding that when the total cost of the mixture is divided by
\n" ); document.write( "the total weight of the mixture, the answer must be $8 per lb.
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\n" ); document.write( "What is the total cost of the mixture. Well, the problem tells you that the mixture will
\n" ); document.write( "contain 12 lbs of coffee that costs $14 per lb. Multiplying the 12 lbs times $14 per pound,
\n" ); document.write( "results in $168 dollars worth of the high value coffee in the mix.
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\n" ); document.write( "You do not know what the weight of the cheap coffee will be. So let's call that weight \"W\".
\n" ); document.write( "At $6 per lb for those W pounds the value of the cheap coffee in the mix must be $6*W.
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\n" ); document.write( "Therefore, the value of the mix is the sum of these two dollar amounts. This is $168 + $6*W.
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\n" ); document.write( "Now let's look at the total weight of the mixture. We know that 12 lbs of the mix is
\n" ); document.write( "the expensive coffee. And we have said that the weight of the cheaper coffee in the mix
\n" ); document.write( "will be identified as W lbs. So the total weight of the mixture will be 12 + W lbs.
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\n" ); document.write( "So if we divide the total cost of the coffee (168 + 6W) by the total weight of the mix
\n" ); document.write( "(12 + W) the answer is to be $8 per lb. In equation form this becomes:
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\n" ); document.write( "\"%28168+%2B+6W%29%2F%2812%2BW%29+=+8\"
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\n" ); document.write( "Get rid of the denominator by multiplying both sides of the equation by (12 + W) to get:
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\n" ); document.write( "\"%28%2812%2BW%29%28168%2B6W%29%29%2F%2812%2BW%29+=+%2812%2BW%29%2A8\"
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\n" ); document.write( "On the left side the (12 + W) in the numerator cancels with the (12 + W) in the denominator.
\n" ); document.write( "And on the right side the quantity the 8 times (12 + W) multiplies out to 96 + 8W. So
\n" ); document.write( "you are left with the equation:
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\n" ); document.write( "\"168+%2B+6W+=+96+%2B+8W\"
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\n" ); document.write( "Get rid of the 8W on the right side by subtracting 8W from both sides to get:
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\n" ); document.write( "\"168+-2W+=+96\"
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\n" ); document.write( "Then get rid of the 168 on the right side by subtracting 168 from both sides. The resulting
\n" ); document.write( "equation becomes:
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\n" ); document.write( "\"-2W+=+-72\"
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\n" ); document.write( "You can now solve for W which is the weight of the cheaper coffee in the mixture by dividing
\n" ); document.write( "both sides of this equation by -2 to get:
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\n" ); document.write( "\"W+=+%28-72%29%2F%28-2%29+=+36\"
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\n" ); document.write( "So to get a mixture worth $8 per pound, if you start with 12 lbs of $14 coffee, you need
\n" ); document.write( "to mix in 36 lbs of coffee that sells for $6 per lb to get the desired mixture.
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\n" ); document.write( "Hope this helps you to understand the problem a little better and that you can track the
\n" ); document.write( "above approach to get the answer.
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