Answer :
To solve this problem, we need to figure out an inequality that helps determine the maximum number of boxes you can put in the elevator along with yourself, without exceeding the maximum weight limit of the elevator.
Here's how we can set up the problem:
1. Maximum weight of the elevator: 1600 pounds
2. Your weight: 145 pounds
3. Weight of each box: 40 pounds
We need to ensure that the total weight of you and the boxes doesn’t exceed 1600 pounds. The total weight in the elevator consists of your weight plus the combined weight of the boxes.
Let's denote the number of boxes as [tex]\( n \)[/tex]. Therefore, the total weight in the elevator can be expressed as:
[tex]\[ \text{Your weight} + \text{Weight of boxes} = 145 + 40n \][/tex]
This total weight has to be less than or equal to the maximum weight of the elevator:
[tex]\[ 145 + 40n \leq 1600 \][/tex]
This inequality is the one we will use. So, the correct answer is option c: [tex]\( 145 + 40n \leq 1600 \)[/tex].
Let's break down how this inequality works:
- 145 represents your weight.
- 40n represents the weight of [tex]\( n \)[/tex] boxes, with each box weighing 40 pounds.
- We want total weight [tex]\( 145 + 40n \)[/tex] to be at most 1600 pounds.
To find the maximum number of boxes:
Rearrange the inequality:
[tex]\[ 40n \leq 1600 - 145 \][/tex]
[tex]\[ 40n \leq 1455 \][/tex]
Now, divide both sides by 40 to solve for [tex]\( n \)[/tex]:
[tex]\[ n \leq \frac{1455}{40} \][/tex]
[tex]\[ n \leq 36.375 \][/tex]
Since you can't have a fraction of a box, round down to the nearest whole number. Therefore, the maximum number of boxes you can bring into the elevator with you is 36.
Here's how we can set up the problem:
1. Maximum weight of the elevator: 1600 pounds
2. Your weight: 145 pounds
3. Weight of each box: 40 pounds
We need to ensure that the total weight of you and the boxes doesn’t exceed 1600 pounds. The total weight in the elevator consists of your weight plus the combined weight of the boxes.
Let's denote the number of boxes as [tex]\( n \)[/tex]. Therefore, the total weight in the elevator can be expressed as:
[tex]\[ \text{Your weight} + \text{Weight of boxes} = 145 + 40n \][/tex]
This total weight has to be less than or equal to the maximum weight of the elevator:
[tex]\[ 145 + 40n \leq 1600 \][/tex]
This inequality is the one we will use. So, the correct answer is option c: [tex]\( 145 + 40n \leq 1600 \)[/tex].
Let's break down how this inequality works:
- 145 represents your weight.
- 40n represents the weight of [tex]\( n \)[/tex] boxes, with each box weighing 40 pounds.
- We want total weight [tex]\( 145 + 40n \)[/tex] to be at most 1600 pounds.
To find the maximum number of boxes:
Rearrange the inequality:
[tex]\[ 40n \leq 1600 - 145 \][/tex]
[tex]\[ 40n \leq 1455 \][/tex]
Now, divide both sides by 40 to solve for [tex]\( n \)[/tex]:
[tex]\[ n \leq \frac{1455}{40} \][/tex]
[tex]\[ n \leq 36.375 \][/tex]
Since you can't have a fraction of a box, round down to the nearest whole number. Therefore, the maximum number of boxes you can bring into the elevator with you is 36.
