Task B-1.3. The school has announced a competition for the best-organized classroom. The amount of the monetary prize will be distributed among the four top-ranked classes so that the first-place winner receives $40 \%$ of the total amount, the second-place winner $\frac{1}{3}$ of the total amount, the third-place winner $\frac{5}{8}$ of the remaining prize amount, and the fourth-place winner 1500 kn. Determine the total monetary prize amount and the prize amount for each of the top three places.
Solution. Let $x$ be the total amount of the monetary prize. Then,

$$
\begin{aligned}
0.4 x+\frac{1}{3} x+\frac{5}{8}\left(x-0.4 x-\frac{1}{3} x\right)+1500 & =x \\
\frac{2}{5} x+\frac{1}{3} x+\frac{1}{6} x+1500 & =x \\
12 x+10 x+5 x+45000 & =30 x \\
3 x & =45000 \\
x & =15000
\end{aligned}
$$

The first prize is 6000 kn, the second prize is 5000 kn, and the third prize is 2500 kn.