Xzavier is competing in a math contest. The math test has 30 questions. The list shows the number of points that can be earned on each question.
Correct answer: +3 points
Incorrect answer: –4 points
No answer: –1 point
Xzavier answered 20 questions on the test. What is the minimum number of questions that Xzavier answered correctly if he earned a positive score?
Let x be the number of questions Xzavier answered correctly.
Since he answered 20 questions in total, the number of questions he answered incorrectly is 20 - x.
His total score can be calculated using the given information:
3x - 4(20 - x) - (30 - 20) > 0
3x - 80 + 4x - 10 > 0
7x - 90 > 0
7x > 90
x > 90 / 7
x > 12.86
Since the number of correct answers must be a whole number, Xzavier must have answered at least 13 questions correctly to earn a positive score.