Question

A grocer wants to make a 20-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?

A. 6
B. 8
C. 12
D. 14

Answer 1

To determine the quantity of cashews needed, we use the sale price of the mix and the individual prices of peanuts and cashews to establish a set of linear equations. Solving these equations reveals that the grocer should use 6 pounds of cashews to make the 20-pound mixture.

Step-by-step explanation:

To solve the question of how many pounds of cashews a grocer should use to make a 20-pound mixture of peanuts and cashews that sells for $4.75 per pound, we need to set up a system of linear equations. Let's define p as the number of pounds of peanuts and c as the number of pounds of cashews. We have two equations:

• The total weight of peanuts and cashews must be 20 pounds: p + c = 20.
• The total value of the mix must be $4.75 per pound: 4.00p + 6.50c = 20 × 4.75.

Simplifying the second equation:

• 4.00p + 6.50c = 95.00.

Since p + c = 20, we can express p as 20 - c. Substituting into the second equation gives us:

• 4.00(20 - c) + 6.50c = 95.00.

Simplifying:

• 80 - 4.00c + 6.50c = 95.00.
• 2.50c = 15.00.
• c = 15.00 / 2.50.
• c = 6.

The grocer should use 6 pounds of cashews for the mixture.