Calculate Test Score: 5, -2, -4 Point System with 20 Questions

A teacher decides to award the following points:

5 points for each correct answer.

-2 for each incorrect answer.

-4 for each unanswered question.

There were 20 questions on the exam.

What is the score of the student who answers all the questions correctly, except for 4 questions that are left unanswered?

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Calculate the number of correct answers
• Step 3: Calculate the score from correct answers
• Step 4: Calculate the score from unanswered questions
• Step 5: Sum the contributions to get the total score

Now, let's work through each step:

Step 1: Identify the given information
The problem states there are 20 total questions, with 5 points for each correct, -2 for each incorrect, and -4 points for each unanswered question. The student left 4 questions unanswered.

Step 2: Calculate the number of correct answers
Since the student answered all questions except 4, the correct number of answers is 20 - 4 = 16.

Step 3: Calculate the score from correct answers
The score for correct answers is $16 \times 5 = 80$ points.

Step 4: Calculate the score from unanswered questions
We have 4 unanswered questions, contributing $4 \times (-4) = -16$ points.

Step 5: Sum the contributions to get the total score
Add the scores from the correct and unanswered questions: $80 + (-16) = 64$.

Therefore, the solution to the problem is $64$.