Question 248299: Peanuts cost $3 per pound, almonds $4 per pound and cashews $8 per pound. How many pounds of each should be used to produce 140 pounds of mixture costing $6 per pound, in which there are twice as many peanuts as almonds?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Peanuts cost $3 per pound, almonds $4 per pound and cashews $8 per pound. How many pounds of each should be used to produce 140 pounds of mixture costing $6 per pound, in which there are twice as many peanuts as almonds?
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Equations:
p = 2a
p + a + c = 140
3p + 4a + 8c = 6*140
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Substitute into the 2nd and the 3rd equation:
3a + c = 140
10a+8c = 840
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Multiply thru the 1st Eq by 8:
24a + 8c = 8*140
10a + 8c = 840
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Subtract the 2nd from the 1st and solve for "a":
14a = 280
a = 20 (amt. of almonds in the mix)
p = 2a = 40 (amt of peanuts in the mix)
c + 3a = 140
c + 60 = 140
c = 80 (amt of cashews in the mix)
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Cheers,
Stan H.
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