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the manager of a health food store sells peanuts for $8 a pound and premium cashews for $15 a pound. if he wishes ti make a 105 pound cashew and peanut mix that will sell for $12 a pound, how many pounds of cashews should he use?

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opudodennis

Answer:

Cashews-75lb

Peanuts-30lb

Step-by-step explanation:

Let x=amount of cashews needed,

Then 105-x=amount of peanuts needed.

#Value of the nuts before the mixture is:

[tex]8(105-x)+15x[/tex]

#The value before the mixture must be equal to the value after mixture:

[tex]V_b=8(105-x)+15x\\\\V_a=105\times12=1260\\\\1260=8(105-x)+15x\\\\1260=840-8x+15x\\\\x=75[/tex]

Hence, the weight of cashews used is 75 lb

#And the weight of peanuts used is 105-75=30lb

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