Pankrác, Servác, and Bonifác bought a boat. Pankrác paid $60\%$ of the boat's price, Servác paid $40\%$ of the remaining price, and Bonifác paid the missing amount, which was 30 gold coins.

How many gold coins did the boat, which the boys bought, cost?

(L. Hozová)
Let the cost of the boat be denoted by $z$. Pankrác paid $\frac{6}{10} z$, leaving

$$
\left(1-\frac{6}{10}\right) z=\frac{4}{10} z
$$

Servác paid $\frac{4}{10} \cdot \frac{4}{10} z=\frac{16}{100} z$, leaving

$$
\left(\frac{4}{10}-\frac{16}{100}\right) z=\frac{24}{100} z=\frac{6}{25} z
$$

The remaining amount was paid by Bonifác, which amounted to 30 gold coins. Thus, $\frac{6}{25} z=30$, from which it follows that $z=125$. The boat cost 125 gold coins.

Note. The previous considerations can be illustrated as follows (the whole represents the cost of the boat, the marked rectangles represent the shares of the individual contributors):

![](https://cdn.mathpix.com/cropped/2024_04_17_76d9fb87d3e1f8305746g-1.jpg?height=457&width=965&top_left_y=1645&top_left_x=548)

Evaluation. 2 points for expressing Pankrác's contribution and the remainder; 2 points for expressing Servác's contribution and the remainder; 2 points for calculating and answering.