A product's price was increased by $p \%$, then during a promotion, it was decreased by $p / 2 \%$; as a result, the product costs only $p / 3 \%$ more than originally. Calculate the value of $p$.

 untranslated portion:
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Egy termék árát $p \%$-kal emelték, majd egy akció során $p / 2 \%$-kal csökkentették; így a termék csak $p / 3 \%$-kal kerül többe, mint eredetileg. Számítsuk ki $p$ értékét.
Let $x$ denote the original price of the product. After a $p \%$ increase, the price is $x\left(1+\frac{p}{100}\right)$, and after the decrease, it is this value multiplied by $\left(1-\frac{p}{2 \cdot 100}\right)$. Therefore,

$$
x\left(1+\frac{p}{100}\right)\left(1-\frac{p}{2 \cdot 100}\right)=x\left(1+\frac{p}{3 \cdot 100}\right)
$$

After dividing by the non-zero $x$ and rearranging:

$$
p\left(\frac{1}{6}-\frac{p}{200}\right)=0
$$

The trivial (and somewhat uninteresting) solution to the problem is $p=0$. Based on the problem statement, the value of $p$ is: $p=\frac{200}{6} \approx 33 \%$.