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.

Step-by-step 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.

$2.80x+5.30y=4.80\times 100$

$2.80x+5.30y=480$          .... (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.

Answer 2

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