Kenny bought a 50-pound bag of chicken feed for $29.98 and a 25-pound bag for $15.49. Can you use proportional reasoning to find the price of a 40-pound bag?

Select the correct response.

Yes, the ratio of $29.98 to $15.49 is the same as the ratio of 50:25.

Volume 90%

Yes, the ratio of $29.98: 50 is the same as the ratio of $15.49:25.

Volume 90%

No, because there is a constant of proportionality.

Volume 90%

No, because there is no constant of proportionality.

To solve this question, let's analyze the proportionality of the given values.

If we were to find a proportional relationship, the cost per pound in each case would need to be the same.

1. **Cost per pound for the 50-pound bag:**  
   \[
   \frac{29.98}{50} = 0.5996 \text{ dollars per pound}
   \]

2. **Cost per pound for the 25-pound bag:**  
   \[
   \frac{15.49}{25} = 0.6196 \text{ dollars per pound}
   \]

Since these costs per pound are not the same, there is no constant ratio (or constant of proportionality) between the cost and weight in this case. This means we cannot directly use proportional reasoning to determine the price of a 40-pound bag based on the prices of the 50-pound and 25-pound bags.

**Correct Answer:**  
- **No, because there is no constant of proportionality.**

Would you like more details or have any questions about this solution?

### Related Questions:
1. How would you calculate the cost of a 40-pound bag if there were a constant of proportionality?
2. What if we knew the average price per pound based on these two bags? Could that be used to estimate a 40-pound bag's cost?
3. Why is it important to check for a constant of proportionality when using proportional reasoning?
4. How would the answer change if both bags had exactly the same price per pound?
5. Can proportional reasoning be applied if we have a third bag size with a different price-per-pound ratio?

**Tip:** Always verify the constant of proportionality before using proportional reasoning to ensure accuracy in such calculations.

Kenny bought a 50-pound bag of chicken feed for $29.98 and a 25-pound bag for $15.49. Can you use proportional reasoning to find the price of a 40-pound bag?

Learn how to solve pricing problems using proportional reasoning with a real-world example. This problem involves calculating the cost per pound for different bag sizes and checking for a constant of proportionality. Suitable for students in Grades 7-9.

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