SOLUTION: A coffee shop is mixing Arabic coffee worth $15.00 per pound with Brazilian coffee worth $22.00 per pound. The combination will sell for $20.00 per pound. To make 100 Pounds of thi

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Question 761892: A coffee shop is mixing Arabic coffee worth $15.00 per pound with Brazilian coffee worth $22.00 per pound. The combination will sell for $20.00 per pound. To make 100 Pounds of this mixture, how much of each type of coffee should be used?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1: In the combination of 100 pounds, let there be x pounds of Arabic.
Step 2: So, the combination has (100 - x) pounds of Brazilian
Step 3: Cost of the mixture = cost of arabic in mix + cost of brazilian in mix
= %2815%2Ax+%2B+22%2A%28100-x%29%29
Step 4: But the cost of the mixture is given to be 20 per pound. Or, cost of 100 pounds of mix = 20%2A100+=+2000
Step 5: The values of step 3 and step 4 have to be equal. Hence we have the equation
%2815%2Ax+%2B+22%28100+-+x%29%29+=+2000
Step 6: Solve for x
15%2Ax+%2B+2200+-+22%2Ax+=+2000
200+=+7%2Ax x+=+200%2F7
So the mixture has 200%2F7 pounds of Arabic and 100+-+200%2F7+=500%2F7 pounds of Brazilian coffee.

:)