Answer :
To solve this problem, we need to write an inequality that represents the situation with the maximum allowable weight for an elevator.
1. Understand the given weights:
- The maximum weight capacity of the elevator is 1600 pounds.
- Your weight is 145 pounds.
- Each box weighs 40 pounds.
2. Set up the inequality:
- The total weight in the elevator includes both your weight and the weight of the boxes.
- If you let [tex]\( n \)[/tex] represent the number of boxes, then the combined weight of the boxes is [tex]\( 40n \)[/tex] pounds.
3. Write the inequality:
- Your weight plus the total weight of the boxes should not exceed the elevator’s maximum capacity. So, the inequality will be:
[tex]\[
145 + 40n \leq 1600
\][/tex]
4. Select the correct answer:
- Compare this inequality to the provided options:
- [tex]\( a. \)[/tex] [tex]\( 1600-145 \leq 40n \)[/tex]
- [tex]\( b. \)[/tex] [tex]\( 145+40n \geq 1600 \)[/tex]
- [tex]\( c. \)[/tex] [tex]\( 145+40n \leq 1600 \)[/tex]
- [tex]\( d. \)[/tex] [tex]\( 1600+145 \geq 40n \)[/tex]
- The correct choice that matches our inequality is option [tex]\( c \)[/tex]: [tex]\( 145+40n \leq 1600 \)[/tex].
Therefore, the inequality that can be used to determine the maximum number of boxes is [tex]\( 145 + 40n \leq 1600 \)[/tex], which corresponds to choice [tex]\( C \)[/tex].
1. Understand the given weights:
- The maximum weight capacity of the elevator is 1600 pounds.
- Your weight is 145 pounds.
- Each box weighs 40 pounds.
2. Set up the inequality:
- The total weight in the elevator includes both your weight and the weight of the boxes.
- If you let [tex]\( n \)[/tex] represent the number of boxes, then the combined weight of the boxes is [tex]\( 40n \)[/tex] pounds.
3. Write the inequality:
- Your weight plus the total weight of the boxes should not exceed the elevator’s maximum capacity. So, the inequality will be:
[tex]\[
145 + 40n \leq 1600
\][/tex]
4. Select the correct answer:
- Compare this inequality to the provided options:
- [tex]\( a. \)[/tex] [tex]\( 1600-145 \leq 40n \)[/tex]
- [tex]\( b. \)[/tex] [tex]\( 145+40n \geq 1600 \)[/tex]
- [tex]\( c. \)[/tex] [tex]\( 145+40n \leq 1600 \)[/tex]
- [tex]\( d. \)[/tex] [tex]\( 1600+145 \geq 40n \)[/tex]
- The correct choice that matches our inequality is option [tex]\( c \)[/tex]: [tex]\( 145+40n \leq 1600 \)[/tex].
Therefore, the inequality that can be used to determine the maximum number of boxes is [tex]\( 145 + 40n \leq 1600 \)[/tex], which corresponds to choice [tex]\( C \)[/tex].
