SOLUTION: How many pounds of nuts selling for $12 per lb and raisins selling for $6 per lb should a person combine to obtain 90 lb of a trail mix selling for $8 per lb?

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Question 1005983: How many pounds of nuts selling for $12 per lb and raisins selling for $6 per lb should a person combine to obtain 90 lb of a trail mix selling for $8 per lb?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of nuts needed
Let +b+ = pounds of raisins needed
-------------------------------
(1) +a+%2B+b+=+90+
(2) +%28+12a+%2B+6b+%29+%2F+90+=+8+
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(2) +12a+%2B+6b+=+720+
(2) +2a+%2B+b+=+120+
--------------------
Subtract (1) from (2)
(2) +2a+%2B+b+=+120+
(1) +-a+-+b+=+-90+
-------------------
+a+=+30+
and
(1) +a+%2B+b+=+90+
(1) +b+=+60+
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30 pounds of nuts are needed
60 pounds of raisins are needed
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check:
(2) +%28+12a+%2B+6b+%29+%2F+90+=+8+
(2) +%28+12%2A30+%2B+6%2A60+%29+%2F+90+=+8+
(2) +%28+360+%2B+360+%29+%2F+90+=+8+
(2) +720+=+8%2A90+
(2) +720+=+720+
OK