746. There are containers of two types: 130 kg and 160 kg. How many containers of the first type and how many of the second type are there if together they weigh 3 tons? List all solutions.
Let's denote the number of containers of the first type by $x$, and the second type by $y$. We get the equation

$$
130 x + 160 y = 3000, \quad 13 x + 16 y = 300
$$

Let's try to use divisibility by 13. For this, we represent $16 y$ as $13 y + 3 y$, and divide 300 by 13 with a remainder:

$$
13 x + 13 y + 3 y = 13 \cdot 23 + 1, \quad 3 y - 1 = 13 \cdot 23 - 13 x - 13 y .
$$

The right side of the last equation is divisible by 13, so the left side must also be divisible by 13. To find the values of $y$ for which the difference $3 y - 1$ is divisible by 13, we will use trial and error. Instead of assigning $y$ consecutive values $1, 2, 3$, etc., it is easier to set $3 y - 1$ to numbers divisible by 13: $13, 26, 39, 52, 65$, etc., and determine each time whether the root of the corresponding equation is an integer or a fraction. Integer roots are obtained in the following cases:

$$
3 y - 1 = 26, \quad y = 9 ; \quad 3 y - 1 = 65, \quad y = 22
$$

and so on. But the value $y = 22$ is already too large, since in this case

$$
16 y = 16 \cdot 22 = 352 > 300 .
$$

For $y = 9$, we can find $x$ from the equation:

$$
13 x + 16 \cdot 9 = 300, \quad 13 x = 156, \quad x = 12
$$

Answer: 12 containers of 130 kg each and 9 of 160 kg each.