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

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

To solve this problem, let's break down the situation:

1. Total Weight Limit: The elevator can hold a maximum weight of 1600 pounds.

2. Your Weight: You weigh 145 pounds.

3. Weight of Each Box: Each box weighs 40 pounds.

Now, let's construct an inequality to determine how many boxes you can take with you:

- First, account for your own weight. Since you weigh 145 pounds, we start with that:
[tex]\[
\text{Total weight in the elevator} = 145 + \text{(weight of boxes)}
\][/tex]

- Let's say [tex]\( n \)[/tex] is the number of boxes. Since each box is 40 pounds, the total weight of the boxes is [tex]\( 40n \)[/tex]:
[tex]\[
\text{Weight of boxes} = 40n
\][/tex]

- The total weight (your weight plus the weight of the boxes) must be less than or equal to the maximum weight capacity of the elevator (1600 pounds):
[tex]\[
145 + 40n \leq 1600
\][/tex]

This inequality [tex]\( 145 + 40n \leq 1600 \)[/tex] can be used to determine the maximum number of boxes you can place in the elevator at one time along with yourself.

Thus, the correct answer from the choices provided is:
- C. [tex]\( 145 + 40n \leq 1600 \)[/tex]

This inequality correctly represents the situation described.