Cashews at $7.40 a pound are mixed with peanuts at $2.60 a pound. If there are 18 pounds in the mixture and the mixture sells for $5.80 per pound, how many pounds of cashews are there in the mixture?

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Cashews at $7.40 a pound are mixed with peanuts at $2.60 a pound. If there are 18 pounds in the mixture and the mixture sells for $5.80 per pound, how many pounds of cashews are there in the mixture?

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Answer 1 · 2015-08-16T21:50:40

I found:
$12$ pounds of cashews
$6$ pounds peanuts

Explanation:

Call $C$ and $P$ the quantities of the two; you have:
${(C+P=18),(7.4C+2.6P=5.8*18=104.4):}$
solve the system (by substitution, for example) to get:
$C=18-P$
$7.4(18-P)+2.6P=104.4$
So:
$P=6$ pounds
$C=12$ pounds

This answers assumes a seller that sells at a price exactly according to the mixture. Many sellers are would be fully willing to sell you a "mixture" that is completely peanuts for them to have a profit. Assuming a seller would not sell for a loss, the answer would be "AT LEAST 6 pounds of peanuts, and AT MOST 12 pounds of cashews".

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Cashews at $7.40 a pound are mixed with peanuts at $2.60 a pound. If there are 18 pounds in the mixture and the mixture sells for $5.80 per pound, how many pounds of cashews are there in the mixture?

1 Answer

Explanation:

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