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

The formula that describes how a student's raw score depends on the number of correct answers is r = 6c - 0.5(40 - c).

Step-by-step explanation:

The formula that describes how a student's raw score, r, depends on the number of correct answers he or she provided, c, is:

r = 6c - 0.5(40 - c)

Let's break down the formula:

1. The number of correct answers, c, is multiplied by 6, since the student gains 6 points for each correct answer.
2. The number of incorrect answers is calculated by subtracting c from the total number of questions, which is 40 in this case.
3. The number of incorrect answers is then multiplied by 0.5, since the student loses 0.5 points for each incorrect answer.
4. The calculated score for correct answers is subtracted from the calculated score for incorrect answers to get the raw score, r.

Answer 2

`\text{r}=5.5\text{c}-20`

Step-by-step explanation:

GIVEN: 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.

TO FIND: the formulas that describes how a student's raw score, r, depends on the number of correct answers he or she provided, c.

SOLUTION:

Total number of incorrect questions
`=40-\text{c}`

Total marks deducted due to incorrect question
`=(40-\text{c})*0.5=20-0.5\text{c}`

Total correct questions
`=\text{c}`

Total marks scored
`=6\text{c}`

Total raw marks
`\text{r}=\text{total marks gained}-\text{total marks deducted}`

`\text{r}=6\text{c}-(20-0.5\text{c})`

`\text{r}=5.5\text{c}-20`

ormulas that describes how a student's raw score, r, depends on the number of correct answers he or she provided, c is
`\text{r}=5.5\text{c}-20`