here is the question: I am confused about the steps I need to follow to be able to complete this question some explanation will be appreciated :)
In a Multiple - choice examination of 25 questions, four marks are
given for each correct answer and two marks are deducted for each
wrong answer. One mark is deducted for any question which is not
attempted.
A candidate attempts q questions and gets c correct.
a) Write down an expression for the candidate's total mark in terms of
q and c.
b) James attempts 22 questions and scores 55 marks. Write down and
solve an equation for the number of questions which James gets right
(b)attempted question=22
left question=3
since the maximum mark can be obtained from attempted questions.
total mark can be obtained=22*4=88
since he has secured 55;so lost mark=88-55=33
since three question he has left;so three must be deducted from attempted question mark.
so 33-3=30
each wrong answer will deduct (4+2=6)marks.
so total no of question attempted but wrong=30/6=5
attempted question =22
so 22-5=17 is the correct ans
To help you understand the steps needed to complete this question, let's break it down into parts.
a) Write down an expression for the candidate's total mark in terms of q and c.
To calculate the total mark, we need to consider the following:
- For each correct answer, the candidate receives 4 marks.
- For each wrong answer, the candidate loses 2 marks.
- For any question not attempted, the candidate loses 1 mark.
Let's break it down into individual components:
- The number of correct answers, c, will contribute 4c to the total mark.
- The number of wrong answers will be (q - c) because it is determined by subtracting the number of correct answers (c) from the total questions attempted (q). So, for each wrong answer, the candidate loses 2 marks. Therefore, the number of marks deducted for wrong answers will be 2(q - c).
- The number of questions not attempted will be (25 - q), and for each not-attempted question, the candidate loses 1 mark. Therefore, the number of marks deducted for not-attempted questions will be (25 - q).
Now, we can write the expression for the candidate's total mark in terms of q and c:
Total Marks = 4c - 2(q - c) - (25 - q)
b) James attempts 22 questions and scores 55 marks. Write down and solve an equation for the number of questions which James gets right.
Let's substitute the given values into the expression to form the equation:
55 = 4c - 2(22 - c) - (25 - 22)
Simplifying the equation:
55 = 4c - 2(22 - c) - 3
Now, solve for c by further simplifying the equation:
55 = 4c - 44 + 2c - 3
58 = 6c - 47
6c = 105
c = 17.5
Since we are dealing with a number of questions, c cannot be a decimal. Therefore, James cannot have a fraction of a correct answer. This implies that James may have answered some questions incorrectly or left them unattempted. However, we can still determine the number of correct answers by rounding down the decimal: c = 17.
Therefore, James answered 17 questions correctly.