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, we want to figure out the maximum number of boxes you can place in an elevator without exceeding its weight limit. Let's break it down step-by-step:

1. Understand the Limits:
- The maximum weight the elevator can hold is 1600 pounds.

2. Account for Your Weight:
- You weigh 145 pounds, which is already part of the total weight in the elevator. So, to calculate the weight allowance for the boxes, we must subtract your weight from the elevator's weight limit:
[tex]\[
\text{Weight available for boxes} = 1600 - 145 = 1455 \text{ pounds}
\][/tex]

3. Determine the Weight of the Boxes:
- Each box weighs 40 pounds.

4. Set Up the Inequality:
- Let [tex]$ n $[/tex] be the number of boxes. The total weight of the boxes will be [tex]$ 40n $[/tex].
- The weight of you and the boxes together should not exceed 1600 pounds. This gives us the inequality:
[tex]\[
145 + 40n \leq 1600
\][/tex]

5. Simplify the Inequality:
- First, subtract your weight from both sides of the inequality:
[tex]\[
40n \leq 1455
\][/tex]

6. Solve for [tex]$ n $[/tex]:
- Divide both sides by 40 to find out the maximum number of boxes:
[tex]\[
n \leq \frac{1455}{40} = 36.375
\][/tex]
- Since you can't have a fractional number of boxes, you can take a maximum of 36 boxes.

Now, based on the options provided, the correct inequality that represents this problem is:
- [tex]$ 145 + 40n \leq 1600 $[/tex]

Thus, the answer is c.