There are 40 questions in a Mathematics competition. For each correct answers, participants are awarded 3 points. 1 mark is deducted for each wrong answer. By forming an inequality, find the minimum number of questions a participant needs to get correct to score 90 points.

Let's denote the number of correct answers by x and the number of wrong answers by y . Given that there are 40 questions in total, we have the equation: x + y = 40 Participants are awarded 3 points for each correct answer and lose 1 point for each wrong answer. To score at least 90 points, we can set up the following inequality: 3x - y \geq 90 We can use the equation x + y = 40 to express y in terms of x : y = 40 - x Substitute y in the inequality: 3x - (40 - x) \geq 90 3x - 40 + x \geq 90 4x - 40 \geq 90 4x \geq 130 x \geq \frac{130}{4} x \geq 32.5 Since x must be an integer (you can't correctly answer a fraction of a question), we round up to the nearest whole number: x \geq 33 Therefore, the minimum number of questions a participant needs to get correct to score at least 90 points is \boxed{33} .