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Answer :
To solve this problem, we need to write an inequality that represents the maximum weight the elevator can carry with both you and the boxes inside.
1. Identify the given values:
- Maximum weight of the elevator: 1600 pounds
- Your weight: 145 pounds
- Weight of each box: 40 pounds
2. Set up the components for the inequality:
- The combined weight of you and the boxes must be less than or equal to the maximum allowed weight of the elevator.
3. Write the inequality:
- Let [tex]\( n \)[/tex] be the number of boxes. The total weight of the boxes is [tex]\( 40n \)[/tex].
- The total weight in the elevator is your weight plus the weight of the boxes, which is [tex]\( 145 + 40n \)[/tex].
- This total weight must be less than or equal to 1600 pounds, so we write the inequality:
[tex]\[
145 + 40n \leq 1600
\][/tex]
Now, let's identify the correct option from the choices provided:
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]
The correct inequality that represents the scenario is option c: [tex]\( 145 + 40n \leq 1600 \)[/tex].
1. Identify the given values:
- Maximum weight of the elevator: 1600 pounds
- Your weight: 145 pounds
- Weight of each box: 40 pounds
2. Set up the components for the inequality:
- The combined weight of you and the boxes must be less than or equal to the maximum allowed weight of the elevator.
3. Write the inequality:
- Let [tex]\( n \)[/tex] be the number of boxes. The total weight of the boxes is [tex]\( 40n \)[/tex].
- The total weight in the elevator is your weight plus the weight of the boxes, which is [tex]\( 145 + 40n \)[/tex].
- This total weight must be less than or equal to 1600 pounds, so we write the inequality:
[tex]\[
145 + 40n \leq 1600
\][/tex]
Now, let's identify the correct option from the choices provided:
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]
The correct inequality that represents the scenario is option c: [tex]\( 145 + 40n \leq 1600 \)[/tex].
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