Question

How many pounds of deluxe mixed nuts worth $8 per pound must be combined with 4 pounds of peanuts worth $3 per pound to create a nut mixture worth $6 per pound? Use p to represent the number of pounds of deluxe nuts.

a) p = 6

b) p = 8

c) p = 10

d) p = 12

Answer 1

To create a nut mixture worth $6 per pound by combining $3 per pound peanuts with $8 per pound deluxe nuts, we need to mix 6 pounds of deluxe nuts with 4 pounds of peanuts.

Step-by-step explanation:

To solve the problem of combining different types of nuts to achieve a desired mixture value, we will set up an equation based on the given values. The deluxe mixed nuts cost $8 per pound, and we need to find how many pounds, represented by p, must be mixed with 4 pounds of peanuts worth $3 per pound to create a mixture that is worth $6 per pound.

The total value of the deluxe nuts would be 8p (since they are $8 per pound), and the total value of the peanuts would be 4 x $3 = $12. When these are combined, the equation to find the new mixture's value is 8p + 12 = 6(p + 4).

Simplifying the equation:

8p + 12 = 6p + 24

8p - 6p = 24 - 12

2p = 12

p = 12 / 2

p = 6

Therefore, p equals 6, which means 6 pounds of deluxe mixed nuts are required.