3. In the neighboring houses on Happy Street in Sunny Village, two families of 10 people each lived, with the average weight of the members of one family being 1 kg more than the average weight of the members of the other family. After the eldest sons from both families left to study in the city, it turned out that the average weight of the remaining members of one of these families was 1 kg more than the average weight of the remaining members of the other family. By how many kilograms is the weight of one of the departed sons greater than the weight of the other? List all possible options and prove that there are no others.
Answer: by 1 kg or by 19 kg.

Solution. The total weight of the members of one of the families before the departure of the elder sons was 10 kg more than the total weight of the members of the other family. If the heavier family remained heavier, then its total weight became 9 kg more than the total weight of the other family, meaning the weight of its departed son was 1 kg more than the other departed son. In the opposite case, its total weight became 9 kg less, meaning the weight of its departed son was 19 kg less than the other departed son.

## Grading Criteria:

- Both answers are provided with full justification - 7 points;
- The correct answer and a generally correct justification are provided, but with gaps or inaccuracies - 5 points;
- One answer is provided with justification - 4 points;
- The correct answer is provided without justification - 2 points;
- An incorrect answer is provided - 0 points.