1. Are there natural numbers $x, y$ and $z$ that satisfy the equation $28 x+30 y+31 z=365$?
1. In a year, there are 12 months. One of them, February, consists of 28 days, four months (April, June, September, November) consist of 30 days, and the remaining 7 months consist of 31 days. Since there are 365 days in a year, we get

$$
28 \cdot 1 + 30 \cdot 4 + 31 \cdot 7 = 365
$$

Comments. $1^{\circ}$. Compare with problem 1 for 10th grade. $2^{\circ}$. There is another solution: $x=2, y=1, z=9$.