Challenge for the smart 🤓🧠

Data (given)

One full container on a scale shows 830 g.

Two half-filled containers together on a scale show 960 g.

“Full” liquid mass per container = unknown .

Empty container mass = unknown .

Reasoning / step-by-step

From the full container:

𝐶 + 𝐿 = 830. C+L=830.

From the two half-filled containers: each has 0.5 𝐿, so together the liquids sum to L. The weight equation is:

2 𝐶 + 0.5 𝐿 + 0.5 𝐿 = 2 𝐶 + 𝐿 = 960.

Substitute 𝐿 L from the first equation into the second. From (1): 𝐿 = 830 − 𝐶 . L=830−C. Put that into (2):

2 𝐶 + ( 830 − 𝐶 ) = 960.

Simplify:

2 𝐶 + 830 − 𝐶 = 960 ⇒ 𝐶 + 830 = 960. 2C+830−C=960⇒C+830=960. So 𝐶 = 960 − 830 = 130.

(Optional check) If 𝐶 = 130 C=130, then 𝐿 = 830 − 130 = 700.

Two half containers:

2 𝐶 + 𝐿 = 2 ⋅ 130 = 260 + 700 = 960 2C+L=2⋅130=260+700=960 ✓

Final answer

The mass of the empty container is 130 g.

Little congratulation (for anyone who guessed it already)

If you guessed 130 g before seeing the solution — well done! 🎉 That was a smart move — excellent intuition and great reasoning skills! 👏

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