SOLUTION: she need to prepare 150 pounds of blended coffee beans selling for 4.97 per pound. she plans to do this by blending together a high-quality bean costing 6.25 per pound and a cheape

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Question 896188: she need to prepare 150 pounds of blended coffee beans selling for 4.97 per pound. she plans to do this by blending together a high-quality bean costing 6.25 per pound and a cheaper quality bean at 3.50 per pound. to the nearest pound, find how much high-quality coffee bean and how much cheaper coffee bean she would blend
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of high-quality coffee bean needed
Let +b+ = pounds of cheaper coffee bean needed
--------------------------------
(1) +a+%2B+b+=+150+
(2) +%28+6.25a+%2B+3.5b+%29+%2F+150+=+4.97+
---------------------------------
(2) +6.25a+%2B+3.5b+=+4.97%2A150+
(2) +6.25a+%2B+3.5b+=+745.5+
(2) +625a+%2B+350b+=+74550+
(2) +25a+%2B+14b+=+2982+
-------------------------
Multiply both sides of (1) by +14+
and subtract (1) from (2)
(2) +25a+%2B+14b+=+2982+
(1) +-14a+-+14b+=+-2100+
---------------------------
+11a+=+882+
+a+=+80.182+
and
(1) +a+%2B+b+=+150+
(1) +b+=+150+-+80.182+
(1) +b+=+69.818+
--------------------
80.182 pounds of high-quality coffee bean are needed
69.818 pounds of cheaper coffee bean are needed
check:
(2) +%28+6.25%2A80.182+%2B+3.5%2A69.818+%29+%2F+150+=+4.97+
(2) +%28+501.138+%2B+244.363+%29+%2F+150+=+4.97+
(2) +745.501+%2F+150+=+4.97+
(2) +745.501+=+745.5+
OK