35. The fish soup prepared by the tourists on the seashore after a successful fishing trip was good, but due to lack of culinary experience, they put too little salt in it, so they had to add salt at the table. The next time they made the same amount of fish soup, they put in twice as much salt as the first time, but even then they had to add salt to the soup at the table, though they used only half as much salt as they did the first time. What fraction of the necessary amount of salt did the cook put in the fish soup the first time?
35. Let the amount of salt that should have been added the first time be $a$ g, and the amount actually added be $x$ g, resulting in a shortage of $(a-x)$ g. Another time, $2x$ g of salt was added, leading to a shortage of $a-2x$. Since the amount of salt added the second time was half of what was added the first time, we have $a-x=(a-2x) \cdot 2$, from which $x=\frac{a}{3}$. Therefore, the first time, $\frac{1}{3}$ of the necessary amount of salt was added to the soup.