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In a Math Olympiad quiz, 5 points are awarded for a correct answer and 2 points are deducted for a wrong answer or if a question is left unanswered. Shirley attempted all 30 questions and her total score for the quiz was not more than 66. Find the maximum number of correct answers she obtained.​

Sagot :

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c and i are the numbers of correct and incorrect responses, respectively.
c+i = 30
i = 30-c

5c-2i ≤ 66
5c-2(30-c) ≤ 66
5c-60+2c ≤ 66
7c ≤ 126
c ≤ 126/7
c ≤ 18

Shirley had at most 18 correct answers.

The maximum number of correct answers she obtained is 18 if in a Math Olympiad quiz, 5 points are awarded for a correct answer and 2 points are deducted for a wrong answer.

What is inequality?

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that:

In a Math Olympiad quiz, 5 points are awarded for a correct answer and 2 points are deducted for a wrong answer or if a question is left unanswered.

Let x and be the number of the correct response.

Let y and be the number of the incorrect response.

c + i

x + y = 30

y = 30 - x

5x - 2y ≤ 66

5x - 2(30 - x) ≤ 66

5x - 60 + 2x ≤ 66

7x ≤ 126

x ≤ 126/7

x ≤ 18

After plotting the above inequality we will get the solution region is:

x ∈ (-∞, 18]

The maximum value of x is 18

Thus, the maximum number of correct answers she obtained is 18 if in a Math Olympiad quiz, 5 points are awarded for a correct answer and 2 points are deducted for a wrong answer.

Learn more about the inequality here:

brainly.com/question/19491153

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