A small​ plane's maximum takeoff weight is 

19001900 

pounds or less. Six passengers weigh an average of 

150150 

pounds each. Use an inequality to find the luggage and cargo weights the plane can carry.




To find the maximum luggage and cargo weights the plane can carry, we need to consider the maximum takeoff weight of the plane and the total weight of the passengers.

### Given:
- Maximum takeoff weight of the plane: 1900 pounds
- Average weight of each passenger: 150 pounds
- Number of passengers: 6

### Steps:
1. Calculate the total weight of the passengers:
   \[
   \text{Total weight of passengers} = 150 \, \text{pounds} \times 6 = 900 \, \text{pounds}
   \]

2. Let \( x \) represent the luggage and cargo weights that the plane can carry.

3. The sum of the passengers' weight and the luggage/cargo weight must be less than or equal to the maximum takeoff weight of the plane.

4. The inequality representing this situation is:
   \[
   900 + x \leq 1900
   \]

5. To find the maximum luggage and cargo weights \( x \), solve the inequality:
   \[
   x \leq 1900 - 900
   \]
   \[
   x \leq 1000
   \]

### Conclusion:
The luggage and cargo weights the plane can carry must be **1000 pounds or less**.

Would you like more details on solving inequalities or any other questions?

Here are five related questions:
1. How would the inequality change if the average passenger weight increased?
2. What if the plane could carry only 1800 pounds? How would that affect the maximum luggage and cargo weight?
3. How can you verify if the plane is overloaded with a certain luggage weight?
4. What is the significance of the inequality sign in this context?
5. How would the problem change if you added another passenger?

**Tip:** When solving inequalities, always remember to check your final answer in the context of the problem to ensure it makes sense.

Learn how to determine the luggage and cargo weights a small plane can carry using an inequality. Understand the relationship between passenger weight, plane capacity, and cargo limits with a step-by-step solution. Suitable for Grades 7-9 students.

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