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Algebra / Systems of two linear equations in two variables Difficulty: Medium

The score on a trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers. If a player answered 40 questions and obtained a score of 50, how many questions did the player answer correctly?

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Explanation

The correct answer is 30. Let x represent the number of correct answers from the player and y represent the number of incorrect answers from the player. Since the player answered 40 questions in total, the equation $x plus y, equals 40$ represents this situation. Also, since the score is found by subtracting the number of incorrect answers from twice the number of correct answers and the player received a score of 50, the equation $2 x minus y, equals 50$ represents this situation. Adding the equations in the system of two equations together yields $open parenthesis, x plus y, close parenthesis, plus, open parenthesis, 2 x minus y, close parenthesis, equals, 40 plus 50$ . This can be rewritten as $3 x equals 90$ . Finally, solving for x by dividing both sides of the equation by 3 yields $x equals 30$ .