SOLUTION: A coffee distributor needs to mix a(n) Queen City coffee blend that normally sells for $9.10 per pound with a Organic Free Trade coffee blend that normally sells for $13.70 per pou

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Question 1054026: A coffee distributor needs to mix a(n) Queen City coffee blend that normally sells for $9.10 per pound with a Organic Free Trade coffee blend that normally sells for $13.70 per pound to create 70 pounds of a coffee that can sell for $13.57 per pound. How many pounds of each kind of coffee should they mix?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of $9.10/lb coffee needed
Let +b+ = pounds of $13.70/lb coffee needed
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(1) +a+%2B+b+=+70+
(2) +%28+9.1a+%2B+13.7b+%29+%2F+70+=+13.57+
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(2) +9.1a+%2B+13.7b+=+13.57%2A70+
(2) +9.1a+%2B+13.7b+=+949.9+
(2) +91a+%2B+137b+=+9499+
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Multiply both sides of (1) by +91+
and subtract (1) from (2)
(2) +91a+%2B+137b+=+9499+
(1) +-91a+-+91b+=+-6370+
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+46b+=+3129+
+b+=+68.022+
and
(1) +a+%2B+b+=+70+
(1) +a+%2B+68.022+=+70+
(1) +a+=+1.978+
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They need 1.978 pounds of Queen City Coffee
They need 68.022 pounds of Organic Free Trade Coffee
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check:
(2) +%28+9.1a+%2B+13.7b+%29+%2F+70+=+13.57+
(2) +%28+9.1%2A1.978+%2B+13.7%2A68.022+%29+%2F+70+=+13.57+
(2) +%28+18+%2B+931.9+%29+%2F+70+=+13.57+
(2) +949.9+%2F+70+=+13.57+
(2) +949.9+=+949.9+
OK
Hope I got it