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 Xzavier answered 20 questions in total, the number of questions he answered incorrectly or left unanswered is 30 - 20 = 10.
To earn a positive score, Xzavier's total points earned must be greater than 0:
3x - 4(10) - 1(30 - x) > 0
3x - 40 - 30 + 4x > 0
7x - 70 > 0
7x > 70
x > 10
So, Xzavier must have answered at least 11 questions correctly to earn a positive score.