MATHEMATICS 1. In a game show, participants receive 6 points for every correct answer and 4 points are deducted for every incorrect answer. If a participant answers 15 questions and ends up with 30 points, how many correct answers did he give?

Let the number of correct answers be \( x \) and the number of incorrect answers be \( y \). Since the participant answers a total of 15 questions, we have the equation: \[ x + y = 15 \] The scoring of the game gives 6 points for each correct answer and deducts 4 points for each incorrect one. Thus, we can express the score as: \[ 6x - 4y = 30 \] Now we have a system of equations to solve: 1. \( x + y = 15 \) 2. \( 6x - 4y = 30 \) From the first equation, we can express \( y \) in terms of \( x \): \[ y = 15 - x \] Substituting this into the second equation gives: \[ 6x - 4(15 - x) = 30 \] \[ 6x - 60 + 4x = 30 \] \[ 10x - 60 = 30 \] \[ 10x = 90 \] \[ x = 9 \] So, the participant gave 9 correct answers. Now, let's verify. If \( x = 9 \), then \( y = 15 - 9 = 6 \). The score would be \( 6(9) - 4(6) = 54 - 24 = 30 \), which matches the given final score. Therefore, the participant answered **9 correct answers**.