A nut wholesaler sells a mix of cashews and peanuts. He charges $2.80 per pound for cashews and $5.30 per pound for peanuts. If the mix is to sell for $3.3 per pound, how many pounds each of peanuts and cashews should be used to make 100 pounds of the mix?
A)The wholesaler should mix 13.4 pounds of peanuts with 61 pounds of cashews.
B)The wholesaler should mix 14 pounds of peanuts with 73.4 pounds of cashews.
C)The wholesaler should mix 26.6 pounds of peanuts with 86 pounds of cashews.
D)The wholesaler should mix 39 pounds of peanuts with 86.6 pounds of cashews.
E)The wholesaler should mix 20 pounds of peanuts with 80 pounds of cashews.

Question

A nut wholesaler sells a mix of cashews and peanuts. He charges $2.80 per pound for cashews and $5.30 per pound for peanuts. If the mix is to sell for $3.3 per pound, how many pounds each of peanuts and cashews should be used to make 100 pounds of the mix? ​
A)The wholesaler should mix 13.4 pounds of peanuts with 61 pounds of cashews.
B)The wholesaler should mix 14 pounds of peanuts with 73.4 pounds of cashews.
C)The wholesaler should mix 26.6 pounds of peanuts with 86 pounds of cashews.
D)The wholesaler should mix 39 pounds of peanuts with 86.6 pounds of cashews.
E)The wholesaler should mix 20 pounds of peanuts with 80 pounds of cashews.

Quizplus · Accepted Answer

To solve this, we use the concept of weighted averages or a system of equations. Let $x$ be the pounds of peanuts and $y$ be the pounds of cashews. We have two equations: $x + y = 100$ (since the total mix is 100 pounds) and $5.3x + 2.8y = 3.3 \times 100$ (to account for the total cost of the mix). Solving these equations or using the method of alligation, we find that the ratio of peanuts to cashews that meets the criteria is 20 pounds of peanuts to 80 pounds of cashews.

A Nut Wholesaler Sells a Mix of Cashews and Peanuts