https://file.aiquickdraw.com/mathbot/file/1726405478192akdnzljj.jpg

Let's go step by step to solve this quiz problem.

### a) Maximum score you could get on the quiz:
To maximize the score, you need to answer all 25 questions correctly. Each correct answer scores 3 points, so:
\[
\text{Maximum score} = 25 \times 3 = 75
\]
This has already been filled in correctly.

### b) Minimum score you could get on the quiz:
To minimize the score, you should answer all 25 questions incorrectly. Each incorrect answer deducts 2 points, so:
\[
\text{Minimum score} = 25 \times (-2) = -50
\]

### c) A student answers 15 questions, 10 are correct:
- For the 10 correct answers, the student scores \( 10 \times 3 = 30 \) points.
- For the 5 incorrect answers (since 15 - 10 = 5), the student loses \( 5 \times 2 = 10 \) points.
\[
\text{Total score} = 30 - 10 = 20
\]

### d) Another student answers 21 questions, 6 are correct:
- For the 6 correct answers, the student scores \( 6 \times 3 = 18 \) points.
- For the 15 incorrect answers (since 21 - 6 = 15), the student loses \( 15 \times 2 = 30 \) points.
\[
\text{Total score} = 18 - 30 = -12
\]

### Final answers:
- a) Maximum score: \( 75 \)
- b) Minimum score: \( -50 \)
- c) Total score for 15 questions (10 correct): \( 20 \)
- d) Total score for 21 questions (6 correct): \( -12 \)

Would you like further details or explanations? 

Here are some related questions for practice:
1. What if a student answers 12 questions, with 8 correct?
2. What is the score if all answers are left blank?
3. If a student answers 20 questions and 7 are correct, what is the score?
4. How many correct answers are needed to ensure a positive score, assuming 25 answers are given?
5. What if a student answers only 5 questions, all incorrect?

**Tip:** Always check the impact of penalties on your score before deciding how many questions to attempt.

There are 25 questions in a quiz. Every correct answer scores 3 points. Each incorrect answer loses 2 points. A question not answered scores 0 points. It is possible to finish the quiz with a negative score. What is the maximum and minimum score you could get on the quiz, and how many points do students score in given scenarios?

Solve a quiz problem with 25 questions where correct answers earn 3 points and incorrect ones deduct 2 points. Find the maximum and minimum scores, and calculate the scores for students who answer specific numbers of correct and incorrect questions.

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