1. A game participant was offered 30 questions. For each correct answer, they were awarded 7 points, and for an incorrect answer (or no answer), 12 points were deducted. How many correct answers did the participant give if they scored 77 points?
1. Let the number of correct answers be $x$, then the number of incorrect answers is $30-x$. We have $7 x-12 \cdot(30-x)=77 ; 19 x=437 ; x=23$.