Answer :
To solve this problem, we need to determine the maximum number of boxes that can be placed in the elevator along with you, without exceeding the weight limit of the elevator.
1. Identify the Total Maximum Weight Allowed
The total weight that the elevator can hold is 1600 pounds.
2. Consider Your Weight
Your weight is 145 pounds, which is part of the total weight in the elevator.
3. Determine the Weight of Each Box
Each box weighs 40 pounds.
4. Set Up the Inequality
To find out how many boxes you can add to the elevator without exceeding the weight limit, we can create an inequality. The combination of your weight and the box weights must be less than or equal to the total maximum weight allowed by the elevator.
So the inequality is:
[tex]\( 145 + 40n \leq 1600 \)[/tex]
Here, [tex]\( n \)[/tex] represents the number of boxes.
5. Solve the Inequality for [tex]\( n \)[/tex]
- Subtract 145 from both sides of the inequality:
[tex]\( 40n \leq 1600 - 145 \)[/tex]
[tex]\( 40n \leq 1455 \)[/tex]
- Divide both sides by 40 to isolate [tex]\( n \)[/tex]:
[tex]\( n \leq \frac{1455}{40} \)[/tex]
6. Calculate [tex]\( n \)[/tex]
Divide 1455 by 40:
[tex]\( n \leq 36.375 \)[/tex]
Since you can't have a fraction of a box in this context, we round down to the nearest whole number:
[tex]\( n \leq 36 \)[/tex]
Therefore, the maximum number of boxes you can place in the elevator along with yourself is 36. The correct inequality from the choices provided that matches our expression is:
c. [tex]\(145 + 40n \leq 1600\)[/tex]
1. Identify the Total Maximum Weight Allowed
The total weight that the elevator can hold is 1600 pounds.
2. Consider Your Weight
Your weight is 145 pounds, which is part of the total weight in the elevator.
3. Determine the Weight of Each Box
Each box weighs 40 pounds.
4. Set Up the Inequality
To find out how many boxes you can add to the elevator without exceeding the weight limit, we can create an inequality. The combination of your weight and the box weights must be less than or equal to the total maximum weight allowed by the elevator.
So the inequality is:
[tex]\( 145 + 40n \leq 1600 \)[/tex]
Here, [tex]\( n \)[/tex] represents the number of boxes.
5. Solve the Inequality for [tex]\( n \)[/tex]
- Subtract 145 from both sides of the inequality:
[tex]\( 40n \leq 1600 - 145 \)[/tex]
[tex]\( 40n \leq 1455 \)[/tex]
- Divide both sides by 40 to isolate [tex]\( n \)[/tex]:
[tex]\( n \leq \frac{1455}{40} \)[/tex]
6. Calculate [tex]\( n \)[/tex]
Divide 1455 by 40:
[tex]\( n \leq 36.375 \)[/tex]
Since you can't have a fraction of a box in this context, we round down to the nearest whole number:
[tex]\( n \leq 36 \)[/tex]
Therefore, the maximum number of boxes you can place in the elevator along with yourself is 36. The correct inequality from the choices provided that matches our expression is:
c. [tex]\(145 + 40n \leq 1600\)[/tex]
