There are 20 question in a quiz. 5 marks will be given for a correct answer.

Question

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.

Answer 1

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

Answer 2

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