Mom was going to bake rolls, all from the same pieces of dough. If she baked three rolls for each child, she would have dough left for two more rolls. If she wanted to bake four rolls for each child, she would be short of dough for one roll.

For how many children was Mom baking rolls?

(L. Hozová)
We will gradually examine the possibilities based on the number of children:

- If she had 1 child, then the dough should yield $1 \cdot 3 + 2 = 5$ and simultaneously $1 \cdot 4 - 1 = 3$ rolls. These values are different, so she did not have 1 child.
- If she had 2 children, then the dough should yield $2 \cdot 3 + 2 = 8$ and simultaneously $2 \cdot 4 - 1 = 7$ rolls. These values are different, so she did not have 2 children.
- If she had 3 children, then the dough should yield $3 \cdot 3 + 2 = 11$ and simultaneously $3 \cdot 4 - 1 = 11$ rolls. These values are the same, so she had 3 children.

For larger numbers of children, equality will not occur, and the difference between the compared values will gradually increase. The mother baked rolls for 3 children.

Note. The previous examination of possibilities can be clearly written as follows ($d$ represents the number of children):

| $d$ | 1 | 2 | $\mathbf{3}$ | 4 | 5 | $\ldots$ |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| $3 d + 2$ | 5 | 8 | $\mathbf{1 1}$ | 14 | 17 | $\ldots$ |
| $4 d - 1$ | 3 | 7 | $\mathbf{1 1}$ | 15 | 19 | $\ldots$ |

The correct possibility can be reached by solving the equation

$$
3 d + 2 = 4 d - 1
$$

Evaluation. 3 points for examining the possibilities for different numbers of children or setting up the equation; 3 points for the correct result.