SOLUTION: A grocer mixes peanuts that cost 1.47 per pound and walnuts that cost 2.67 per pound to make 100 pounds of mixture that cost 2.43 per pound.how much of each kind is put into the mi

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Question 988546: A grocer mixes peanuts that cost 1.47 per pound and walnuts that cost 2.67 per pound to make 100 pounds of mixture that cost 2.43 per pound.how much of each kind is put into the mixture
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of peanuts needed
Let +b+ = pounds of walnuts needed
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(1) +a+%2B+b+=+100+
(2) +%28+1.47a+%2B+2.67b+%29+%2F+100+=+2.43+
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(2) +1.47a+%2B+2.67b+=+243+
(2) +147a+%2B+267b+=+24300+
Multiply both sides of (1) by +147+
and subtract (1) from (2)
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(2) +147a+%2B+267b+=+24300+
(1) +-147a+-+147b+=+-14700+
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+120b+=+9600+
+b+=+80+
and
(1) +a+%2B+80+=+100+
(1) +a+=+20+
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20 pounds of peanuts are needed
80 pounds of walnuts are needed
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check:
(2) +%28+1.47a+%2B+2.67b+%29+%2F+100+=+2.43+
(2) +%28+1.47%2A20+%2B+2.67%2A80+%29+%2F+100+=+2.43+
(2) +%28+29.4+%2B+213.6+%29+%2F+100+=+2.43+
(2) +243%2F100+=+2.43+
(2) +243+=+243+
OK