SOLUTION: A storekeeper wishes to sell 100 pounds of mixed nuts for $1.75 a pound. He mixes peanuts worth $1.65 a pound with cashews worth $1.90 a pound. How many pounds of each does he use?

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Question 1005331: A storekeeper wishes to sell 100 pounds of mixed nuts for $1.75 a pound. He mixes peanuts worth $1.65 a pound with cashews worth $1.90 a pound. How many pounds of each does he use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of peanuts used
Let
(2) +%28+165a+%2B+190b+%29+%2F+100+=+175+ ( in cents )
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(2) +165a+%2B+190b+=+17500+
(2) +33a+%2B+38b+=+3500+
Multiply both sides of (1) by +33+ and subtract (1) from (2)
(2) +33a+%2B+38b+=+3500+
(1) +-33a+-+33b+=+-3300+
------------------------
+5b+=+200+
+b+=+40+
and
(1) +a+%2B+b+=+100+
(1) +a+=+60+
60 pounds of peanuts are used
40 pounds of cashews are used
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check:
(2) +%28+165a+%2B+190b+%29+%2F+100+=+175+
(2) +%28+165%2A60+%2B+190%2A40+%29+%2F+100+=+175+
(2) +%28+9900+%2B+7600+%29+%2F+100+=+175+
(2) +17500+=+175%2A100+
(2) +17500+=+17500+
OK