Solve the problem.
The maximum weight for an elevator is 1600 pounds. You need to move boxes each weighing 40 pounds, and you weigh 145 pounds. Write an inequality that can be used to determine the maximum number of boxes that you can place in the elevator at one time. Assume only you and the boxes are in the elevator.
a. $1600-145 \leq 40 n$
b. $145+40 n \geq 1600$
c. $145+40 n \leq 1600$
d. $1600+145 \geq 40 n$
Please select the best answer from the choices provided
Answer (2)
Define n as the number of boxes.
Express the total weight in the elevator as the sum of the person's weight and the weight of the boxes: 145 + 40 n .
Set up the inequality: 145 + 40 n ≤ 1600 .
The correct answer is c. 145 + 40 n ≤ 1600
Explanation
Problem Analysis Let's analyze the problem. We are given the maximum weight an elevator can hold, the weight of a person, and the weight of each box. We need to find an inequality that represents the maximum number of boxes that can be safely placed in the elevator with the person.
Setting up the Inequality Let n be the number of boxes. The total weight of the boxes is 40 n pounds. The total weight in the elevator is the sum of the person's weight and the weight of the boxes, which is 145 + 40 n pounds. Since the total weight must be less than or equal to the maximum weight the elevator can hold, we have the inequality 145 + 40 n ≤ 1600 .
Finding the Correct Option Comparing our inequality 145 + 40 n ≤ 1600 with the given options, we see that it matches option c.
Final Answer Therefore, the correct answer is c. 145 + 40 n ≤ 1600 .
Examples
Imagine you're loading a delivery van with packages. You know the van's maximum weight capacity and the weight of each package. This problem is similar to figuring out how many packages you can load without exceeding the van's limit. By setting up an inequality, you can determine the maximum number of packages, ensuring you stay within the safe weight limit. This helps prevent overloading, which could damage the vehicle or pose a safety risk.
The inequality representing the maximum number of boxes you can place in the elevator is 145 + 40 n ≤ 1600 . The correct answer from the options provided is option c. This inequality ensures the total weight does not exceed the elevator's weight limit.
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