Answer:
Number of 2-point questions = 30
Number of 4-point questions = 10
Step-by-step explanation:
Let the number of 2 point questions =
Let the number of 4 point questions =
Sum equation:
Total number of questions can be given by =
Total number of questions = 40
So, we have :
Points equation:
Total points for number of 2 point question =
Total points for number of 4 point question =
Total points in the test can be given by =
Total points in the test = 100
So, we have :
So, the system of equations is:
A)
B)
Rearranging equation A, to solve for in terms of
Subtracting both sides by
Substituting value of we got from A into equation B.
Using distribution.
Simplifying.
Subtracting both sides by 160.
Dividing both sides by -2.
We can plugin in the rearranged equation A to get value of
∴
Thus, number of 2-point questions = 30
Number of 4-point questions = 10