Solve the problem:

The maximum weight for an elevator is 1600 pounds. You need to move boxes each weighing 40 pounds, and you weigh 145 pounds. Write an inequality that can be used to determine the maximum number of boxes that you can place in the elevator at one time. Assume only you and the boxes are in the elevator.

A. [tex]145 + 40n \leq 1600[/tex]
B. [tex]1600 - 145 \leq 40n[/tex]
C. [tex]145 + 40n \geq 1600[/tex]
D. [tex]1600 + 145 \geq 40n[/tex]

Please select the best answer from the choices provided:
A
B
C
D

To solve the problem, we need to determine the maximum number of boxes that can be placed in the elevator along with your weight without exceeding the elevator's maximum capacity. Here's how you can set up the problem:

1. Understand the Maximum Capacity: The elevator can hold up to 1600 pounds.

2. Account for Your Weight: You weigh 145 pounds, which means part of the elevator's weight capacity is used for your weight.

3. Calculate the Remaining Capacity: Subtract your weight from the elevator's maximum capacity to find out how many pounds are available for the boxes.
[tex]\[
1600 - 145 = 1455 \, \text{pounds available for the boxes}
\][/tex]

4. Determine the Box Weight: Each box weighs 40 pounds.

5. Set Up the Inequality: We use an inequality to represent the situation where the cumulative weight of the boxes plus your weight should not exceed 1600 pounds. In inequality form, it looks like this:
[tex]\[
145 + 40n \leq 1600
\][/tex]
- Here, [tex]$ n $[/tex] represents the number of boxes.

6. Choose the Correct Option: The inequality from step 5 matches option c. Therefore, the correct answer is option c:
[tex]\[
145 + 40n \leq 1600
\][/tex]

This inequality accurately describes the maximum number of boxes you can have in the elevator along with yourself without exceeding the weight limit.