In two rooms of an educational center, lectures were being held. The average age of eight people present in the first room was 20 years, and the average age of twelve people in the second room was 45 years. During the lecture, one participant left, and as a result, the average age of all people in both rooms increased by one year. How old was the participant who left?

(L. Hozová)
According to the problem, the sum of the ages of eight people present in the first room was $8 \cdot 20=160$ years, and the sum of the ages of twelve people present in the second room was $12 \cdot 45=540$ years. Therefore, the average age of all the people in both rooms was $\frac{160+540}{8+12}=\frac{700}{20}=$ $=35$ years.

If $x$ represents the age of the person who left during the lecture, then we know that

$$
\frac{700-x}{20-1}=35+1
$$

and we solve the equation:

$$
\begin{aligned}
700-x & =36 \cdot 19, \\
x & =700-684=16 .
\end{aligned}
$$

The participant who left was 16 years old.