1. The sum of two numbers is 2022. If the last digit 5 of the first number is erased, and the digit 1 is appended to the right of the second number, the sum of the modified numbers will become 2252. Find the original numbers.
Answer: 1815 and 207.

Solution. Let the original numbers be $x$ and $y$. We form the system

$$
\left\{\begin{array}{l}
x+y=2022 \\
\frac{x-5}{10}+10 y+1=2252
\end{array}\right.
$$

Solving the system, we find $x=1815, y=207$.

Comment. Correct solution - 20 points. Solution is not complete, but there is progress - 5 points. Correct answer found by trial and error, without showing that there are no other values - 5 points. Solution started, but progress is insignificant - 1 point.