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Algebra 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.