Let the fineness of the alloys be denoted by $x, y, z$. Their silver content: $5 x, 3 y, 2 z$ (in kg). According to the statements in the problem,

$$
\begin{aligned}
& 5 x+3 y=0.750(5+3)=6 \ldots \\
& 5 x+2 z=0.780(5+2)=5.46 \ldots \\
& 2 z+3 y=0.852(2+3)=4.26 \ldots
\end{aligned}
$$

Multiply the terms of (3) by -1 and then add the corresponding terms of the three equations; the result is:

$$
10 x=6+5.46-4.26=7.20 \text { and hence } x=0.720 \text {. }
$$

Subtract the terms of (2) from the sum of the terms of (1) and (3):

$$
6 y=6+4.26-5.76=4.80, \text { so } y=0.800
$$

Subtract the terms of (1) from the sum of the terms of the other two:

$$
4 z=5.46+4.26-6=3.72 \text { and thus } z=0.930 .
$$

Lajos Stúr (Bencés g. V. o. Kőszeg).
We have three types of silver and copper castings; their weights are $5,3,2 \mathrm{~kg}$. By melting the first two together, we obtain an alloy with a fineness of 0,760; the first and third, 0,780; the second and third, 0,852.

What is the fineness of the castings available to us?