Task A-1.2. (8 points)

If we add the digit 3 to the left of a two-digit number, the resulting number is 27 times greater than twice the given two-digit number.

Determine that two-digit number.
## Solution.

Let $\overline{x y}=10 x+y$ be the desired two-digit number. We have

$$
\begin{gathered}
2 \cdot \overline{3 x y}=27 \cdot \overline{x y} \\
2 \cdot(300+\overline{x y})=27 \cdot \overline{x y} \\
600+2 \cdot \overline{x y}=27 \cdot \overline{x y} \\
600=25 \cdot \overline{x y}
\end{gathered}
$$

The desired number is $\overline{x y}=24$.

For 4 points: the problem is well set up, at least $\left({ }^{*}\right)$ or equivalent.

For 8 points: the correct result and procedure.