Answer :
To solve this problem, let's break it down step-by-step:
1. Identify the total weight capacity of the elevator:
The maximum weight the elevator can hold is 1600 pounds.
2. Consider your weight:
You weigh 145 pounds. This means that when you're in the elevator, 145 pounds of the total capacity is already used.
3. Calculate the remaining weight capacity for the boxes:
To find out how much weight is available for the boxes, subtract your weight from the total capacity:
[tex]\(1600 - 145 = 1455\)[/tex] pounds.
4. Recognize the weight of each box:
Each box weighs 40 pounds.
5. Write the inequality:
You want to find how many boxes, represented by [tex]\(n\)[/tex], can fit in the elevator without exceeding the weight limit. Since each box weighs 40 pounds, the total weight of the boxes will be [tex]\(40n\)[/tex].
6. Set up the inequality:
The sum of your weight plus the weight of the boxes must not exceed the elevator’s capacity. So,
[tex]\(145 + 40n \leq 1600\)[/tex].
This inequality represents the maximum number of boxes you can take with you in the elevator at one time. Thus, the correct choice from the options provided is option C: [tex]\(145 + 40n \leq 1600\)[/tex].
1. Identify the total weight capacity of the elevator:
The maximum weight the elevator can hold is 1600 pounds.
2. Consider your weight:
You weigh 145 pounds. This means that when you're in the elevator, 145 pounds of the total capacity is already used.
3. Calculate the remaining weight capacity for the boxes:
To find out how much weight is available for the boxes, subtract your weight from the total capacity:
[tex]\(1600 - 145 = 1455\)[/tex] pounds.
4. Recognize the weight of each box:
Each box weighs 40 pounds.
5. Write the inequality:
You want to find how many boxes, represented by [tex]\(n\)[/tex], can fit in the elevator without exceeding the weight limit. Since each box weighs 40 pounds, the total weight of the boxes will be [tex]\(40n\)[/tex].
6. Set up the inequality:
The sum of your weight plus the weight of the boxes must not exceed the elevator’s capacity. So,
[tex]\(145 + 40n \leq 1600\)[/tex].
This inequality represents the maximum number of boxes you can take with you in the elevator at one time. Thus, the correct choice from the options provided is option C: [tex]\(145 + 40n \leq 1600\)[/tex].
