Question

Shipping brothers incorporated charges customers based on the weight of their package the charge $5 for shipping packages that are less than 30 lb they charge $10 for shipping packages that are 30 lbs to less than 50 lb they charge $15 for shipping packages that are 50 pounds or less than 75 lb they charged $20 for shipping packages that are $75 pounds or heavier based on the graph find approximate interval of can't for $410 shipping rate

Answer 1

To determine the approximate interval of weight for a shipping charge of $410 based on the provided pricing structure, let’s break it down:

1. **Weight < 30 lb**: $5
2. **30 lb ≤ Weight < 50 lb**: $10
3. **50 lb ≤ Weight < 75 lb**: $15
4. **Weight ≥ 75 lb**: $20

To find the weight range for a shipping rate of $410:

1. **Calculate how much of $410 goes towards each weight category**:
- For **packages under 30 lb**: Each package costs $5. Therefore:
\[
\text{Number of packages} = \frac{410}{5} = 82 \text{ packages}
\]
- For **packages between 30 lb and 50 lb**: Each package costs $10. Therefore:
\[
\text{Number of packages} = \frac{410}{10} = 41 \text{ packages}
\]
- For **packages between 50 lb and 75 lb**: Each package costs $15. Therefore:
\[
\text{Number of packages} = \frac{410}{15} \approx 27.33 \text{ packages}
\]
- For **packages 75 lb or heavier**: Each package costs $20. Therefore:
\[
\text{Number of packages} = \frac{410}{20} = 20.5 \text{ packages}
\]

2. **Interpreting these results**:
- If shipping for packages less than 30 lb, 82 packages could be shipped.
- If for packages between 30 lb and 50 lb, it would be 41 packages.
- For packages between 50 lb and 75 lb, around 27 packages can be shipped.
- For heavier packages (75 lb and above), around 20 packages can be shipped.

Since the question is about the shipping rate of $410, we can conclude:
- The shipping rate of $410 could be applicable for packages weighing **at least 75 lbs**, but the actual shipping cost indicates that the total weight could be varying based on how many packages you are sending.

**Conclusion**:
You can send up to 20 packages that weigh 75 lbs each, or you may have a combination of lighter packages leading up to a total shipping cost of $410 within the defined weight ranges.

The interval of weight for the $410 shipping cost primarily uniquely matches or exceeds 75 lbs per package since this category typically charges the highest rate ($20). However, you could also send multiple packages in smaller weight categories that add up to $410 in shipping costs under different weight combinations.