A store is mixing up two types of nuts, peanuts and cashews into a 50 lb barrel. peanuts sell for $4 a pound and cashews sell for $7 a pound. If the store wants to sell the mix for $5.75 a pound, how many pounds of each nut should be put into the mix?

Question

Mathematics

Byron Washington

12 September, 09:30

A store is mixing up two types of nuts, peanuts and cashews into a 50 lb barrel. peanuts sell for $4 a pound and cashews sell for $7 a pound. If the store wants to sell the mix for $5.75 a pound, how many pounds of each nut should be put into the mix?

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Answers (1)

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Jadyn Maxwell · Answer 1

Cashew 12.5lb

Peanuts 37.5lb

Step-by-step explanation:

Let the number of pounds of cashewnuts and peanuts be c and p respectively.

Firstly, the total mass of the nuts is 50.

This means:

c + p = 50

Now let's work with the money

4p + 7c = 4.75 (50)

From the first equation, let c = 50 - p

Substitute this into the second equation.

4p + 7 (50 - p) = 237.5

4p + 350 - 7p = 237.5

3p = 112.5

P = 112.5/3 = 37.5lb

For Cashew c = 50 - p = 50 - 37.5 = 12.5lb