Anička has 50 Kč, Anežka has 46 Kč, and they want to buy snacks for a family celebration with all their money. They are deciding between cupcakes and windmills: a windmill is 4 Kč more expensive than a cupcake, and with all their money, they could buy a third more cupcakes than windmills.

How much does each snack cost?

(M. Volfová)

Hint. In how many ways can Anička and Anežka spend all their money without any remainder?
Anička and Anežka together have 96 Kč. This amount can only be spent in a few ways, which are derived from expressing the number 96 as a product of two natural numbers:

$$
96=1 \cdot 96=2 \cdot 48=3 \cdot 32=4 \cdot 24=6 \cdot 16=8 \cdot 12 \text {. }
$$

The price of a kite and the price of a cake should correspond to numbers with a difference of 4. Such pairs of numbers are only three among the given factors (marked in bold):

$$
\mathbf{2} \cdot 48=\mathbf{6} \cdot 16, \quad \mathbf{4} \cdot 24=\mathbf{8} \cdot 12, \quad 6 \cdot \mathbf{1 6}=8 \cdot \mathbf{1 2} .
$$

In the first case, the girls would choose between 48 cakes at 2 Kč each and 16 kites at 6 Kč each; however, 48 is not one third more than 16, so this option does not work.

In the second case, the girls would choose between 24 cakes at 4 Kč each and 12 kites at 8 Kč each; however, 24 is not one third more than 12, so this option also does not work.

In the third case, the girls would choose between 8 cakes at 12 Kč each and 6 kites at 16 Kč each; 8 is one third more than 6, so this is the only viable option.

One cake costs 12 Kč, and one kite costs 16 Kč.

Another solution. For the same amount of money, one can buy one third more cakes than kites, meaning that for the price of 3 kites, one can buy 4 cakes. A kite is 4 Kč more expensive than a cake, so 3 kites cost 12 Kč more than 3 cakes. From this, it follows that 12 Kč plus the price of 3 cakes equals the price of 4 cakes. Therefore, a cake costs 12 Kč. A kite costs 4 Kč more, so 16 Kč.

(For verification: for 96 Kč, the girls can buy $96: 16=6$ kites or $96: 12=8$ cakes.)

Note. For those who can express the conditions from the problem using variables, we add:

If we denote the price of a cake by $d$ (Kč), then a kite costs $d+4$ (Kč). If the number of kites that can be bought with all the money is denoted by $k$, then the number of cakes that can be bought for the same amount of money is $\frac{4}{3} k$. From the problem, we know that

$$
k \cdot(d+4)=\frac{4}{3} k \cdot d
$$

From this, it follows that $3 d+12=4 d$, so $d=12$, and $d+4=16$.