Question

A nut wholesaler sells a mix of peanuts and cashews. He charges $2.80 per pound for peanuts and $5.30 per pound for cashews. If the mix is to sell for $4.80 per pound, how many pounds each of peanuts and cashews should be used to make 100 pounds of the mix?

Answer 1

Answer: 20 pounds of peanuts and 80 pounds of cashews.

Answer 2

20 pounds of peanuts and 80 pounds of cashews.

Explanation:

A nut wholesaler sells a mix of peanuts and cashews.

We need to find the amount of peanuts and cashews should be used to make 100 pounds of the mix.

Let x pounds of peanuts y pounds of cashews are mixed.

`x+y=100` .... (1)

He charges $2.80 per pound for peanuts and $5.30 per pound for cashews. If the mix is to sell for $4.80 per pound.

`2.80x+5.30y=4.80* 100`

`2.80x+5.30y=480` .... (2)

From (1) we get

`x=100-y` .... (3)

Substitute this value in equation (2).

`2.80(100-y)+5.30y=480`

`280-2.80y+5.30y=480`

`2.50y=480-280`

`2.50y=200`

Divide both sides by 2.50.

`y=80`

Substitute y=80 in equation (3).

`x=100-80=20`

Therefore, 20 pounds of peanuts and 80 pounds of cashews should be used to make 100 pounds of the mix.