SOLUTION: Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 29 pounds of feed worth $ 0.37 per pound by mixing one kind worth $ 0.29 per pound with another worth $ 0.4

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Question 679337: Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 29 pounds of feed worth $ 0.37 per pound by mixing one kind worth $ 0.29 per pound with another worth $ 0.46 per pound. How many pounds of the cheaper kind should they use in the mix?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of $.29 / lb feed needed
Let +b+ = pounds of $.46 / lb feed needed
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given:
(1) +a+%2B+b+=+29+
(2) +%28+.29a+%2B+.46b+%29+%2F+29+=+.37+
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(2) +.29a+%2B+.46b+=+.37%2A29+
(2) +.29a+%2B+.46b+=+10.73+
(2) +29a+%2B+46b+=+1073+
Multiply both sides of (1) by +29+
and subtract (1) from (2)
(2) +29a+%2B+46b+=+1073+
(1) +-29a+-+29b+=+-841+
+17b+=+232+
+b+=+13.65+
and, since
(1) +a+%2B+13.65+=+29+
(1) +a+=+15.35+
They should use 15.35 pounds of the cheaper feed
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check answer:
(2) +%28+.29a+%2B+.46b+%29+%2F+29+=+.37+
(2) +%28+.29%2A15.35+%2B+.46%2A13.65+%29+%2F+29+=+.37+
(2) +%28+4.45+%2B+6.28+%29+%2F+29+=+.37+
(2) +10.73+%2F+29+=+.37+
(2) +10.73+=+.37%2A29+
(2) +10.73+=+10.73+
OK