Weighing problem with partial fill levels: A vessel full of water weighs 16.5 kg. When the vessel is 1/4 full, it weighs 5.25 kg. What is the weight of the empty vessel (in kg)?

Introduction / Context:
This is a classic linear relation problem involving a container’s own weight and the weight contributed by the water inside it. By comparing the vessel’s weight when full and when partially filled, we can solve for the vessel’s empty weight directly using a simple equation.

Given Data / Assumptions:

• Weight when full: 16.5 kg.
• Weight when 1/4 full: 5.25 kg.
• Let the empty vessel weight be W kg and the water when full be (16.5 − W) kg.

Concept / Approach:
The total weight equals vessel weight plus water weight. At 1/4 full, the water contributes one-fourth of the full-water weight. Form an equation for the 1/4-full condition and solve for W. It is a straightforward application of proportional filling and linear equations.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 1.125: This is 0.75W, not W.
• 4.5 or 3: Overestimates the vessel mass; contradicts the 1/4-full condition.

Common Pitfalls:

• Mistaking 1/4 of the total weight for 1/4 of the water weight.
• Arithmetic slip when rearranging W − 0.25W.

Final Answer: