9.2. A merchant bought several bags of salt in Tver and sold them in Moscow with a profit of 100 rubles. With all the money earned, he again bought salt in Tver (at the Tver price) and sold it in Moscow (at the Moscow price). This time the profit was 120 rubles. How much money did he spend on the first purchase?
Answer: 500 rubles.

First method. Let the cost of a kilogram of salt in Tver be $x$ rubles, and in Moscow $-y$ rubles, and let the merchant buy $a$ kg of salt the first time. Then, according to the condition, $a(y-x)=100$.

The revenue amounted to $ay$ rubles, so the second time the merchant was able to buy $\frac{ay}{x}$ kg of salt. In this case, the profit was $\frac{ay}{x} \cdot y - ay = \frac{ay(y-x)}{x}$ rubles. According to the condition, $\frac{ay(y-x)}{x}=120$.

From the two equations obtained, it follows that $\frac{100y}{x}=120$, that is, $y=\frac{6}{5}x$. Substituting this result into the first equation, we get $ax=500$.

Second method. Let the merchant pay $x$ rubles for the salt during the first purchase in Tver. Then he sold it in Moscow for $x+100$ rubles. The second time he spent $x+100$ rubles in Tver, and received $x+100+120=x+220$ rubles in Moscow. Since the ratio of Moscow and Tver prices did not change, we set up the proportion: $\frac{x}{x+100}=\frac{x+100}{x+220}$. Solving the equation, we get $x=500$.

+ complete justified solution

$\pm$ correct solution with minor gaps or unclear places

干 correct answer obtained based on reasoning with specific numerical data

干 correct answer provided and only verified that it satisfies the condition

- only the answer is provided or the answer with unclear calculations without explanations

If the student assumes that the same number of whole bags was always bought and considers the price of one bag, the grade is not reduced.