12 its of mixed nuts conturing 70% peanuts were mixed with 8ids.of another kind of mixed nuts that contain 40% peanuts.What percent of the new mixture is peanuts 

To find the percentage of peanuts in the new mixture, we can use a weighted average of the peanut percentages based on the amounts of each kind of mixed nuts.

1. **Amount of peanuts in the first mixture:**
   - The first mixture is 12 lbs and contains 70% peanuts.
   - Amount of peanuts in this mixture:  
     \[
     12 \times 0.70 = 8.4 \text{ lbs of peanuts}.
     \]

2. **Amount of peanuts in the second mixture:**
   - The second mixture is 8 lbs and contains 40% peanuts.
   - Amount of peanuts in this mixture:  
     \[
     8 \times 0.40 = 3.2 \text{ lbs of peanuts}.
     \]

3. **Total weight of the new mixture:**
   - Total weight of both mixtures:  
     \[
     12 + 8 = 20 \text{ lbs}.
     \]

4. **Total amount of peanuts in the new mixture:**
   - Total peanuts:  
     \[
     8.4 + 3.2 = 11.6 \text{ lbs of peanuts}.
     \]

5. **Percentage of peanuts in the new mixture:**
   \[
   \frac{11.6}{20} \times 100 = 58\% \text{ peanuts}.
   \]

Thus, the new mixture contains **58% peanuts**.

Would you like more details or have any other questions?

Here are 5 related questions to explore:
1. What would happen if the second mixture had 50% peanuts?
2. How would the result change if the first mixture weighed only 10 lbs?
3. What percentage of peanuts would result if both mixtures were 50% peanuts?
4. What if the total weight was 30 lbs instead of 20 lbs?
5. How would you handle this problem if there were 3 different mixtures?

**Tip:** In weighted average problems, remember to multiply the percentage by the corresponding weight and then divide by the total weight to find the final percentage.

12 lbs of mixed nuts containing 70% peanuts were mixed with 8 lbs of another kind of mixed nuts that contain 40% peanuts. What percent of the new mixture is peanuts?

This problem calculates the percentage of peanuts in a new mixture by combining 12 lbs of nuts containing 70% peanuts and 8 lbs of nuts containing 40% peanuts. The solution demonstrates the use of the weighted average formula to find that 58% of the new mixture is peanuts. Ideal for students in Grades 6-8.

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