Problem 4. As is known, balance scales come to equilibrium when the weight on both pans is the same. On one pan, there are 9 identical diamonds, and on the other, 4 identical emeralds. If one more such emerald is added to the diamonds, the scales will be balanced. How many diamonds will balance one emerald? The answer needs to be justified.
Answer: 3 diamonds.

Solution. From the condition of the problem, it follows that 9 diamonds and 1 emerald weigh as much as 4 emeralds. Thus, if we remove one emerald from each side of the scales, the equality will be preserved, that is, 9 diamonds weigh as much as 3 emeralds. This means that 3 diamonds weigh as much as 1 emerald.

## Criteria

1 p. The correct answer is obtained.

4 p. The correct answer and justification are present.

If the work mentions (or illustrates) three cases of balance on the scales:

- 9 diamonds and 1 emerald balance 4 emeralds,
- 9 diamonds balance 3 emeralds,
- 3 diamonds balance 1 emerald,

then this is considered a correct justification.