The price of gas was raised three times in the first half of the year, by $5\%$, $6\%$, and $10\%$ respectively. Analysts predicted that the gas price would increase by a total of 1/3 over the course of the year. According to this, what percentage increase in the price of gas can be expected for the rest of the year?
Solution. Currently, the price of gas is $x$ forints per $\mathrm{m}^{3}$. After three increases, it will be $1.05 \cdot 1.06 \cdot 1.1 \cdot x$ forints.

Suppose the price will be increased by another $p \%$, and this increase will be one-third of the price. We can then write the following equation:

$$
1.05 \cdot 1.06 \cdot 1.1 \cdot \frac{100+p}{100} \cdot x=\frac{4}{3} \cdot x
$$

Perform the indicated operations $(x \neq 0)$, and after simplification:

$$
(100+p) \cdot 1.2243=\frac{400}{3}, \quad 367.29+3.6729 p=400
$$

From this, $p \approx 8.91$. Therefore, we can expect an additional increase of nearly $9 \%$.