Question

a test has 80 questions . there is one mark for a correct answer ,while there is negative penalty of -1/2 for a wrong answer and -1/4 for an unattempted question .what is the number of questions answered correctly, if the student has scored a net total of 34.5 marks

Answer 1

If \(x,y,z\) are the numbers of questions answered correctly, incorrectly, or not answered (respectively), then you can set up the following system:
\[\begin{cases}x+y+z=80\\
x-0.5y-0.25z=34.5
\end{cases}\]
Are we missing any part to the question?

Answer 2

options a. 45
b. 48
c. 54
d. cannot be determined

Answer 3

Ah alright then. You have two equations with three unknowns. The system has no particular solution; at best you can only solve for two variables in terms of the third variable.

Answer 4

cannot be determined?

Answer 5

yes

Answer 6

but the book shows ans 54

Answer 7

Either that's a typo, or the question is missing some info.

Answer 8

part b que. if the student has left 10 quetions unanswered ,the number of correct answers are a.45,b.48,c.54 d.cannot be determined

Answer 9

10 unanswered questions means \(z=10\) in the equations above:
\[\begin{cases}x+y+10=80\\
x-0.5y-0.25(10)=34.5
\end{cases}~~\iff~~\begin{cases}x+y=70\\
x-0.5y=32
\end{cases}\]
This is a system with 2 equations and 2 unknowns. You can find a numerical value for \(x\).

Answer 10

48