In a quiz with 20 questions, the final score is computed as followed: 1 point for each

Question

In a quiz with 20 questions, the final score is computed as followed: 1 point for each corrected answer, 0 points for each unanswered question and -0.5 points (0.5 points are taken away) for each wrong answer. How many wrong answers did Paul have, if he answered ALL the ‘’questions and got only 14 as final score?

Answer 1

Let n be the number of correct answers. So, 20 - n must be the number of wrong answers, since the quiz had 20 questions. You get 1 point for each correct answer and 1/2 point taken away for each wrong answer. If his total score is 14, we can write:

 

(1)(number of correct) -0.5(number wrong) = 14

 

or

 

(1)(n) - (0.5)(20 - n) = 14

 

n - 10 + 0.5n = 14

 

Add the n's together and add 10 to each side of the equation. We get

 

1.5n = 24

 

Divide both sides of the equation by 1.5. We get

 

n = 16. correct answers.

 

So, he got 20 - n = 20 - 16 = 4 wrong answers