2870 korona is to be divided into 4 parts, so that the ratio of the parts is as follows:

$$
A: C=2: 3, \quad D: B=3: 4, \quad C: E=4: 5, \quad D: A=6: 5
$$
From the given ratios, it follows that

$$
D=\frac{6}{5} A, \quad B=\frac{8}{5} A, \quad C=\frac{3}{2} A, \quad E=\frac{15}{8} A
$$

thus

$$
A+\frac{8}{5} A+\frac{3}{2} A+\frac{6}{5} A+\frac{15}{8} A=2870
$$

from which

$$
A=400 K, \quad \text{so} \ B=640 K, \quad C=600 K, \quad D=480 K, \quad E=750 K
$$

(Imre Kürti, Eger.)

Number of solutions: 36.