Inequalities in One Unknown

There are 20 multiple-choice questions in a quiz.5 marks are given toeach correct answer, 2 marks are deducted for each wrong answer and 1 mark is deducted foreach unattempted question. Doris finished the quizwith two unattempted questions. If she obtains more than 60 marks in the quiz, what is the minimum numberof questions she has answered correctly?


Let n be the number of question she has answered correctly.
Then, number of question she has answer wrongly = 20 - (n + 2) = 18 - n

Marks obtained in the quiz :
5n - 2(18 - n) - 1*2 > 60
5n - 36 + 2n - 2 > 60
7n > 98
n > 14
Hence, minimum value of n = 15

The minimum number of questions she has answered correctly = 15

Let the number of questions she has answered
correctly be x.
then, the number of questions she has answered
wrong is 18-x

so, 5x-2-2(18-x)>60
7x-38>60
x>14

so, the minimum number she has answered correctly is 15