https://file.aiquickdraw.com/mathbot/file/17263501945903ljh8g35.jpg

Let's address each part of the question from the uploaded photo:

### Part A
**Situation**: A freight elevator can hold a maximum weight of 2,500 pounds. We're asked to write an inequality to represent this.

**Solution**:
Let \( w \) represent the weight allowed on the elevator. The inequality that represents the situation would be:
\[ w \leq 2500 \]
This inequality means that the weight on the elevator should be less than or equal to 2,500 pounds.

### Part B
**Situation**: A deliveryman weighs 150 pounds and is delivering cartons that weigh 24 pounds each. We need to determine how many such cartons he can safely put on the elevator at one time.

**Solution**:
Let \( c \) be the number of cartons. The deliveryman's weight plus the weight of the cartons must be less than or equal to the maximum weight the elevator can handle. The inequality can be written as:
\[ 150 + 24c \leq 2500 \]

### Part C
**Solving the Inequality from Part B**:
\[ 150 + 24c \leq 2500 \]
Subtract 150 from both sides to isolate the term involving \( c \):
\[ 24c \leq 2350 \]
Now, divide both sides by 24 to solve for \( c \):
\[ c \leq \frac{2350}{24} \approx 97.9167 \]

**Interpretation**:
The deliveryman can safely put approximately 97 cartons on the elevator at one time (since he cannot put a fraction of a carton).

### Explanation and Results
For each part, the formulation of the inequality and its solution is directly related to ensuring the safety limit of the elevator's weight capacity is not exceeded. The calculations help in making practical decisions about how many cartons can be transported safely in one go.

Would you like more detailed explanations on any part, or do you have any further questions?

Here are some additional questions to consider:
1. What would the situation be if the weight of each carton was different?
2. How would the inequality change if the maximum weight capacity of the elevator was increased?
3. What would be the impact if the deliveryman's weight changed?
4. How does rounding affect the safety margin in real-world applications?
5. What are other factors that could influence how many cartons can be loaded onto the elevator?

**Tip**: When solving inequalities, always remember to consider the units involved and ensure they are consistent throughout your calculations.

A freight elevator can hold a maximum weight of 2,500 pounds. Let w be the weight allowed on the elevator. Write an inequality that represents this situation. A deliveryman weighs 150 pounds. He is delivering cartons that each weigh 24 pounds. He wants to know how many cartons he can safely put on the elevator at one time. Let c represent the number of cartons. Write an inequality that represents this situation.

Solve a problem involving a freight elevator with a 2,500-pound weight capacity. Learn how to write inequalities to represent this situation and determine how many cartons, each weighing 24 pounds, can be safely transported along with a 150-pound deliveryman.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation