There are 20 question in a quiz. 5 marks will be given for a correct answer.
1 mark will be deducted for a blank answer and 3 marks will be deducted for a wrong answer.
(a) Peter gives 2 blank answers and he gets 72 marks. Find the number of correct answers he get.
(b) Is it possible for Thomas to answer all the question and get zero mark?
Explain your answer.
correct --- x
wrong ---- y , both x and y must be whole numbers
x+y+2 = 20
x+y = 18 , #!
5x - 3y - 2 = 72
5x - 3y = 74 , #2
#1 times 3 --> 3x+3y=54
#2 as is -----> 5x - 3y = 74
add them
8x = 128
x = 16
back in #1
16+y=18
y = 2
a) he got 16 right, and 2 wrong, skipping 2
check: 5(16) - 3(2) - 2(1) = 72
b) To answer all the questions and get a 0 :
x+y = 20
5x-3y=0
3x+3y = 60
5x -3y = 0
8x = 60
x = 60/8 , which is not a whole number,
Thus it is not possible
A) Reiny i think first part has the answer:-
He gave 14.4 answers correct and got 72 marks.
B) Yes it is possible as he he answered all the questions, thus in the question it is not mentioned that he gave all the correct answers. And he scored zero
(a) To solve this problem, we need to consider the scoring scheme for the quiz. Let's denote the number of correct answers that Peter gets as "x".
For a blank answer, 1 mark is deducted. Since Peter gives 2 blank answers, a total of 2 marks will be deducted.
For a wrong answer, 3 marks are deducted. Therefore, the number of wrong answers can be calculated by subtracting the number of correct answers from the total number of questions: 20 - x.
The total marks obtained by Peter can be calculated using the given scoring scheme:
Total Marks = (Number of Correct Answers * Marks for Correct Answer) - (Number of Blank Answers * Marks for Blank Answer) - (Number of Wrong Answers * Marks for Wrong Answer)
Substituting the given values into the formula, we get:
72 = (x * 5) - (2 * 1) - ((20 - x) * 3)
Simplifying the equation:
72 = 5x - 2 - 60 + 3x
72 = 8x - 62
8x = 134
x = 16.75
Since the number of correct answers cannot be fractional, we round down to the nearest whole number. Therefore, Peter got 16 correct answers.
(b) It is not possible for Thomas to answer all the questions and get zero mark. Since each question has a negative penalty for a wrong answer and even for a blank answer, Thomas will definitely have some points deducted.
If Thomas answers all the questions, he will have to get at least one of them wrong or leave it blank. In either case, he will receive a negative score based on the given scoring scheme. Hence, it is not possible to obtain zero marks by attempting all the questions.