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 determine the maximum number of boxes you can place in the elevator, we need to consider the total weight of you and the boxes, and make sure it does not exceed the elevator’s maximum weight limit of 1600 pounds.

Here's how we can set up the problem:

1. Identify the known weights:
- Your weight = 145 pounds
- Weight of each box = 40 pounds

2. Set up the inequality:
- The total weight in the elevator is your weight plus the total weight of the boxes.
- Let [tex]$ n $[/tex] be the number of boxes. The total weight in the elevator will be your weight plus [tex]$ 40n $[/tex] (since each box weighs 40 pounds).

3. Express the weight condition as an inequality:
- The total weight of you and the boxes should not exceed the maximum weight limit of the elevator, which is 1600 pounds. Therefore, the inequality is:

[tex]\[
145 + 40n \leq 1600
\][/tex]

4. Interpret the options:
- If we compare our inequality [tex]$ 145 + 40n \leq 1600 $[/tex] with the choices provided, it matches option C.

Therefore, the correct inequality that represents the situation is:

c. [tex]$ 145 + 40n \leq 1600 $[/tex]

This inequality can be used to determine the maximum number of boxes you can safely place in the elevator along with yourself.