Question
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Yanyin is loading identical boxes onto a pallet. Each box weighs 35 pounds, and the pallet can hold a maximum of 1,500 pounds. Which of the following inequalities best describes \( x \), the number of boxes Yanyin can load onto the pallet? Choose 1 answer: (A) \( x+35 \geq 1,500 \) (B) \( x+35 \leq 1,500 \) (C) \( 35 x \geq 1,500 \) (D) \( 35 x \leq 1,500 \)

Ask by Pope Elliott. in the United States
Jan 23,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The correct inequality is \( 35x \leq 1,500 \).

Solution

To determine the correct inequality that represents the number of boxes \( x \) Yanyin can load onto the pallet, let's analyze the given information: 1. **Weight of Each Box:** Each box weighs 35 pounds. 2. **Maximum Weight Capacity:** The pallet can hold a maximum of 1,500 pounds. The total weight of \( x \) boxes can be calculated as: \[ \text{Total weight} = 35x \] Since the pallet can hold up to 1,500 pounds, the total weight must be less than or equal to 1,500 pounds: \[ 35x \leq 1,500 \] Therefore, the correct inequality is: **(D) \( 35x \leq 1,500 \)** Answer: (D) \( 35 x \leq 1,500 \)

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Bonus Knowledge

To determine the maximum number of boxes Yanyin can load onto the pallet, we need to consider that each box weighs 35 pounds and the total weight of the boxes must not exceed the pallet's capacity of 1,500 pounds. Therefore, the correct inequality is \( 35x \leq 1,500 \). This means that if we multiply the number of boxes \( x \) by the weight per box (35 pounds), the product must be less than or equal to 1,500 pounds, making the correct answer (D). Now, if Yanyin loads more boxes than the maximum allowed, it could lead to not only structural failure of the pallet but also potential safety hazards. Loading wisely ensures that both the boxes and the pallet remain secure, allowing for a smooth transportation process. For additional insights, it's interesting to note that weight distribution on a pallet is crucial in logistics. Proper loading techniques prevent tipping during transit, which can be both costly and dangerous. Engaging with logistics professionals or attending workshops can enhance skills in efficient loading and safety practices.

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