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]1600 - 145 \leq 40n[/tex]
b. [tex]145 + 40n \geq 1600[/tex]
c. [tex]145 + 40n \leq 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 of determining the maximum number of boxes you can place in the elevator, we need to set up an inequality based on the weights involved.

1. Understand the problem components:
- The maximum weight capacity of the elevator is 1600 pounds.
- Each box weighs 40 pounds.
- Your weight is 145 pounds.

2. Set up the inequality:

To find out how many boxes (let's call the number of boxes `n`) you can bring into the elevator without exceeding its weight limit, you need to consider the combined weight of you and the boxes.

The total weight in the elevator when you and the boxes are inside can be expressed as:

[tex]\[
\text{Your weight} + \text{Weight of boxes} \times \text{Number of boxes} \leq \text{Maximum elevator weight}
\][/tex]

Plugging in the known values:

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

3. Simplify if necessary (not required here for the inequality itself but for solving it):

To solve this inequality for `n`, you would subtract your weight from both sides:

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

[tex]\[
40n \leq 1455
\][/tex]

This shows that the weight of the boxes combined must not exceed 1455 pounds.

4. Match the inequality with the options given:

The inequality [tex]\(145 + 40n \leq 1600\)[/tex] is given as option C in the problem statement.

Therefore, the correct answer is option C.