Problem 7.1. Sasha and Vanya are playing a game. Sasha asks Vanya questions. If Vanya answers correctly, Sasha gives him 7 candies. If Vanya answers incorrectly, he gives Sasha 3 candies. After Sasha asked 50 questions, it turned out that each of them had as many candies as they had at the beginning. How many questions did Vanya answer correctly?
Answer: 15.

Solution. Let Vanya answer correctly to $x$ questions, then he answered incorrectly to $50-x$ questions. This means that during the game, Vanya received $7 x$ candies and gave away $3(50-x)$ candies. Since the total number of candies for both boys did not change after the game, we get $7 x=3(50-x)$. Solving this, we find $x=15$.

Remark. The same answer could have been obtained by understanding that to "balance the candies," Vanya should "compensate" every 3 correct answers with 7 incorrect ones.