SOLUTION: The Manager of a bulk foods establishment sells a trail mix for $8 per pound and premium cashews for $14 per pound. The manager wishes to make a 225-pound trail mix-cashew mixture

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Question 600774: The Manager of a bulk foods establishment sells a trail mix for $8 per pound and premium cashews for $14 per pound. The manager wishes to make a 225-pound trail mix-cashew mixture that will sell for $11 per pound. how many pounds of each should be used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of trail mix needed
Let +b+ = pounds of cashews needed
+8a+ = cost of trail mix used
+14b+ = cost of cashews used
---------
(1) +a+%2B+b+=+225+
(2) +%28+8a+%2B+14b+%29+%2F+225+=+11+
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(2) +8a+%2B+14b+=+11%2A225+
(2) +8a+%2B+14b+=+2475+
multiply both sides of (1) by +8+ and
subtract (1) from (2)
(2) +8a+%2B+14b+=+2475+
(1) +-8a+-+8b+=+-1800+
+6b+=+675++
+b+=+112.5+
and, since
(1) +a+%2B+b+=+225+
(1) +a+%2B+112.5+=+225+
(1) +a+=+112.5+
112.5 pounds of each should be used
check:
(2) +%28+8%2A112.5+%2B+14%2A112.5+%29+%2F+225+=+11+
(2) +%28+900+%2B+1575+%29+%2F+225+=+11+
(2) +2475+%2F+225+=+11+
(2) +2475+=+2475+
OK