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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

Answer :

To determine the maximum number of boxes you can place in the elevator at one time, we need to consider the total weight the elevator can hold, which should not exceed 1600 pounds.

1. Identify Personal and Box Weights:
- Your weight is 145 pounds.
- Each box weighs 40 pounds.

2. Set Up the Inequality:
- Since the total weight in the elevator includes your weight and the weight of the boxes, we set up an inequality to represent this total weight.
- Let [tex]\( n \)[/tex] be the number of boxes. The total weight of the boxes will then be [tex]\( 40n \)[/tex] pounds.

3. Write the Expression for Total Weight:
- The total weight in the elevator is your weight plus the weight of the boxes: [tex]\( 145 + 40n \)[/tex].

4. Define the Maximum Weight Constraint:
- The elevator can hold a maximum of 1600 pounds. Thus, the total weight must not be more than 1600 pounds, giving us the inequality:
[tex]\[
145 + 40n \leq 1600
\][/tex]

5. Identify the Correct Inequality:
- The inequality [tex]\( 145 + 40n \leq 1600 \)[/tex] matches choice (C).

So, the correct answer is C: [tex]\( 145 + 40n \leq 1600 \)[/tex].

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