Question

The Nutty Professor sells cashews for $6.30 per pound and Brazil nuts for $5.20 per pound. How much of each type should be used to make a 23 pound mixture that sells for $5.73 per pound?

Answer 1

To find the amount of cashews (C pounds) and Brazil nuts (B pounds) for a 23-pound mixture selling at $5.73 per pound, we solve the system of equations C + B = 23 and 6.30C + 5.20B = 131.79. Upon doing so, we will find the precise quantities of each type of nut needed to create the desired mixture.

Step-by-step explanation:

The solution to this problem involves setting up a system of equations based on the given prices and total weight of the mixture. Let's call the amount of cashews to be used C pounds and the amount of Brazil nuts B pounds. According to the problem, we want a 23-pound mixture that sells for $5.73 per pound. Hence, we have two equations:

1. For the total weight of the mixture:
C + B = 23

2. For the total cost of the mixture per pound:
6.30C + 5.20B = 5.73 \(\times\) 23

By solving these equations, we can find the exact pounds of cashews and Brazil nuts needed. We multiply the second equation by 23 so that we equate the cost of the whole 23-pound mixture, which amounts to $131.79 (23 \(\times\) $5.73).

• Multiply the second equation by 23 to scale it:
• 
  
• 6.30C + 5.20B = 131.79
• 
  

This yields a system of the following two equations:

• C + B = 23
• 6.30C + 5.20B = 131.79

We can solve this system using substitution or elimination methods, which should give us the values for C and B.