SOLUTION: a coffee house has 20 pounds of a coffee that sells for $4 per pound. How many pounds of a coffee that sells for $8 per pound should be mixed with the 20 pounds of $4 per pound cof

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Question 575957: a coffee house has 20 pounds of a coffee that sells for $4 per pound. How many pounds of a coffee that sells for $8 per pound should be mixed with the 20 pounds of $4 per pound coffee to obtain a blend that will sell for $5 per pound? How much of the $5 per pound coffee is there to sell?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = pounds of $8/lb coffee needed
+8x+ = cost of the $8/lb coffee
+4%2A20+=+80+ = cost of the $4/lb coffee used
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+%28+8x+%2B+80+%29+%2F+%28+x+%2B+20+%29+=+5+
+8x+%2B+80+=+5%2A%28+x+%2B+20+%29+
+8x+%2B+80+=+5x+%2B+100+
+3x+=+20+
+x+=+6.667+
6 and 2/3 pounds of $8/lb coffee is needed
This makes +6.667+%2B+20+=+26.667+
There is 26 and 2/3 pounds of the $5 /lb coffee to sell
check:
+%28+8x+%2B+80+%29+%2F+%28+x+%2B+20+%29+=+5+
+%28+8%2A6.667+%2B+80+%29+%2F+%28+6.667+%2B+20+%29+=+5+
+%28+53.333+%2B+80+%29+%2F+%28+26.667+%29+=+5+
+133.333+=+5%2A26.667+
+133.333+=+133.333+
OK