SOLUTION: Alan's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Alan $4.20 per pound, and type B coffee costs $5.30 per pound. This month, Alan made

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Question 815076: Alan's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Alan $4.20 per pound, and type B coffee costs $5.30 per pound. This month, Alan made 156 pounds of the blend, for a total cost of 756.40 . How many pounds of type B coffee did he use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of type A coffee needed
Let +b+ = pounds of type B coffee needed
------------
(1) +a+%2B+b+=+156+
(2) +4.2a+%2B+5.3b+=+756.4+
------------------------
(2) +42a+%2B+53b+=+7564+
Multiply both sides of (1) by +42+
and subtract (1) from (2)
(2) +42a+%2B+53b+=+7564+
(1) +-42a+-+42b+=+-6552+
+11b+=+1012+
+b+=+92+
and, since
(1) +a+%2B+b+=+156+
(1) +a+%2B+92+=+156+
(1) +a+=+64+
He used 92 pounds of type B coffee
check:
(2) +4.2%2A64+%2B+5.3%2A92+=+756.4+
(2) +268.8+%2B+487.6+=+756.4
(2) +756.4+=+756.4+
OK