SOLUTION: Macadamia nuts cost $16.50 per pound, but research by an independent firm says that mixed nuts sell better if macadamias are included. The standard mix costs $9.25 per pound. Fin

Algebra ->  Finance -> SOLUTION: Macadamia nuts cost $16.50 per pound, but research by an independent firm says that mixed nuts sell better if macadamias are included. The standard mix costs $9.25 per pound. Fin      Log On


   



Question 915407: Macadamia nuts cost $16.50 per pound, but research by an independent firm says that mixed nuts sell better if macadamias are included. The standard mix costs $9.25 per pound. Find how many pounds of macadamias and how many pounds of the standard mix should be combined to produce 40 pounds that will costs $10 per pound. Find the amounts to the nearest tenth of a pound.
This is soo confusing.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There is just lots of words -some of them not needed
Let +a+ = pounds of macadamias needed
Let +b+ = pounds of standard mix needed
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(1) +a+%2B+b+=+40+
(2) +%28+16.5a+%2B+9.25b+%29+%2F+40+=+10+
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(2) +16.5a+%2B+9.25b+=+400+
(2) +1650a+%2B+925b+=+40000+
(2) +66a+%2B+37b+=+1600+
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Multiply both sides of (1) by +37+
and subtract (1) from (2)
(2) +66a+%2B+37b+=+1600+
(1) +-37a+-+37b+=+-1480+
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+29a+=+120+
+a+=+4.138+
and, since
(1) +a+%2B+b+=+40+
(1) +b+=+35.862+
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4.1 pounds of macadamias are needed
35.9 pounds of standard mix are needed
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check answer:
(2) +%28+16.5a+%2B+9.25b+%29+%2F+40+=+10+
(2) +%28+16.5%2A4.1+%2B+9.25%2A35.9+%29+%2F+40+=+10+
(2) +%28+67.65+%2B+332.08+%29+%2F+40+=+10+
(2) +399.73+=+400+
Error due to rounding off -I think
Hope this helps