## Task 4 - 340524

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0146.jpg?height=232&width=608&top_left_y=1837&top_left_x=724)

On a scale, five empty mineral water bottles on the left are in balance with two full bottles on the right (see illustration).

(a) Britta fills two empty bottles with mineral water and then achieves balance again by adding empty bottles to the right scale.

How many empty bottles are these?

(b) Jan then empties one of the bottles on the right and removes one empty bottle from the left scale. Which scale now tilts downward?

(c) Pia takes all the bottles off the scale and then places two full bottles and one empty bottle on the left, and one full bottle and three empty bottles on the right.

Which scale now tilts downward?
(a) If three more empty bottles are added to the right, then both the left and the right will have two full and three empty bottles; thus, equilibrium is achieved. The number sought is therefore 3.

(b) If we imagine removing the weight of two empty bottles from both scales in the diagram from the problem text, it follows:

Three empty bottles have the same weight as the mineral water that fills two bottles. This leads to the statement:

An empty bottle has a smaller weight than the water for one bottle. Since Jan removes the bottle on the left and the water on the right, and equilibrium prevailed before, the left scale now tilts downward.

(c) The setup that Pia makes can also be derived from the setup reached in (b) by removing one empty bottle from both the left and the right.

Therefore, in Pia's setup, the left scale also tilts downward.

Solutions from the second round of 1994 taken from [5]

### 2.35.3 Third Round 1994, Class 5