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 this problem, we need to write an inequality that represents the maximum weight the elevator can carry with both you and the boxes inside.

1. Identify the given values:
- Maximum weight of the elevator: 1600 pounds
- Your weight: 145 pounds
- Weight of each box: 40 pounds

2. Set up the components for the inequality:
- The combined weight of you and the boxes must be less than or equal to the maximum allowed weight of the elevator.

3. Write the inequality:
- Let [tex]$ n $[/tex] be the number of boxes. The total weight of the boxes is [tex]$ 40n $[/tex].
- The total weight in the elevator is your weight plus the weight of the boxes, which is [tex]$ 145 + 40n $[/tex].
- This total weight must be less than or equal to 1600 pounds, so we write the inequality:
[tex]\[
145 + 40n \leq 1600
\][/tex]

Now, let's identify the correct option from the choices provided:

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]

The correct inequality that represents the scenario is option c: [tex]$ 145 + 40n \leq 1600 $[/tex].