Káta wants to give presents to her friends and is thinking: if I bought each of them a hair clip for 28 Kč, I would still have 29 Kč left, but if it were a teddy bear for 42 Kč, I would be short of 13 Kč. How many friends does Káta have and how much money does she have for gifts?

(M. Volfová)
The difference in the price of a gift for one friend is $42-28=14$ (CZK). The difference in the total price that Káta would pay for gifts for all her friends is $29+13=42$ (CZK). If we multiply the difference in the price of a gift for one friend by the number of friends, we get the difference in the total price. Therefore, the number of friends is determined as the result of dividing the difference in the total price by the difference in the price of both gifts, i.e., $42: 14=3$. Káta has 3 friends.

If she bought a hair clip for 28 CZK for each of them, she would have 29 CZK left, so she has $3 \cdot 28+29=84+29=113$ (CZK).

Note. The final calculation can also be done as follows: if she bought a teddy bear for 42 CZK for each of them, she would be short by 13 CZK, so she would have $3 \cdot 42-13=126-13=113$ (CZK).

The problem can also be solved by experimenting or using equations.

Evaluation. 1 point for the difference in the price of gifts for one friend (i.e., 14 CZK); 2 points for the total difference for all friends (i.e., $42 \mathrm{CZK}); 2$ points for determining and justifying the number of friends; 1 point for determining the amount of money Káta has for gifts.