SOLUTION: A coffee shop has pure Kona beans that sell for ​$45per pound. The owner wants to create 50 pounds of a Kona blend mixture that can be sold for ​$31 per pound by

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Question 1025311: A coffee shop has pure Kona beans that sell for
​$45per pound. The owner wants to create
50 pounds of a Kona blend mixture that can be sold for
​$31 per pound by mixing the Kona beans with some regular beans that sell for
​$10per pound. How many pounds of each bean should the owner​ use?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of Kona beans needed
Let +b+ = pounds of regular beans needed
---------------------
(1) +a+%2B+b+=+50+
(2) +%28+45a+%2B+10b+%29+%2F+50+=+31+
---------------------------
(2) +45a+%2B+10b+=+31%2A50+
(2) +45a+%2B+10b+=+1550+
(2) +9a+%2B+2b+=+310+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +9a+%2B+2b+=+310+
(1) +-2a+-+2b+=+-100+
---------------------
+7a+=+210+
+a+=+30+
and
(1) +a+%2B+b+=+50+
(1) +b+=+20+
30 pounds of Kona beans are needed
20 pounds of regular beans are needed
--------------
check:
(2) +%28+45%2A30+%2B+10%2A20+%29+%2F+50+=+31+
(2) +%28+1350+%2B+200+%29+%2F+50+=+31+
(2) +1550+=+31%2A50+
(2) +1550+=+1550+
OK