To solve this problem, we need to set up an equation that relates the cost of the nuts and the chocolate-coated candies in the mixture.

Let:

• $x$ be the number of pounds of nuts.
• The price of nuts is $3 per pound.
• You are mixing $x$ pounds of nuts with 34 pounds of chocolate-coated candies that cost $0.75 per pound.
• The desired cost of the mixture is $1.42 per pound.

Step-by-step process:

1. The cost of the nuts is $3x$ dollars (since the nuts cost $3 per pound).
2. The cost of the 34 pounds of chocolate-coated candies is $0.75 \times 34 = 25.5$ dollars.
3. The total weight of the mixture is $x + 34$ pounds.
4. The total cost of the mixture is the sum of the costs of the nuts and the chocolate-coated candies: $3x + 25.5$ dollars.
5. The cost per pound of the mixture is the total cost divided by the total weight, which should equal $1.42 per pound.

Thus, the equation is: $\frac{3x + 25.5}{x + 34} = 1.42$

This equation solves for $x$, the number of pounds of nuts needed.

Would you like me to go through solving this equation?

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Here are 5 related questions to deepen your understanding:

1. What if the cost per pound of the mixture was $1.50? How would that affect the equation?
2. What if the amount of chocolate-coated candies was 40 pounds instead of 34 pounds?
3. How do you solve rational equations like this one?
4. How would the equation change if the price of the nuts increased to $4 per pound?
5. What would happen if both the price of nuts and the price of chocolate-coated candies increased?

Tip: When mixing items with different costs, always consider the total weight and cost to set up your equation.