Question

On a 40 question test students gain 6 points for each correct answer and lose 0.5 points on each incorrect answer. If everyone required to give an answer to each question, what is the formulas that describes how a student's raw score, r, depends on the number of correct answers he or she provided, c?

Answer 1

Answer:

r=6.5c-20

Step-by-step explanation:

The raw score is given by

r=c*6-0.5(40-c)

Taking the number of correct answers as c

The incorrect answers will be 40-c

Since each incorrect answer deducts 0.5 points. Then the deducted points will be 0.5(40-c)=20-0.5c

Since correct answers, c gives 6 points each then the number of points will be 6c

Now, the raw score will be

r=6c-(20-0.5c)

Opening the brackets, the signs change hence

r=6c-20+0.5c

r=6.5c-20

Answer 2

The formula that describes the student's raw score based on the number of correct answers is; r = 6.5c - 20

How to solve algebra word problems?

We are told that they gain 6 points for each correct answer and lose 0.5 points for each incorrect answer. Thus, the formula for the raw score is;

The raw score is given by

r = 6c - 0.5(40 - c)

where;

c is the number of correct answers

40 - c as number of incorrect answers

We are told that each incorrect answer deducts 0.5 points.

Thus, the deducted points = 0.5(40 - c) = 20 - 0.5c

We are told that each correct answers, c gives 6 points each. Thus, the raw score will be;

r = 6c - (20 - 0.5c)

⇒ r = 6c  - 20 + 0.5c

r = 6.5c - 20

Read more about algebra word problems at; https://brainly.com/question/13818690