Answer:
Number of 2-point questions = 30
Number of 4-point questions = 10
Step-by-step explanation:
Let the number of 2 point questions = ![x](https://tex.z-dn.net/?f=x)
Let the number of 4 point questions = ![y](https://tex.z-dn.net/?f=y)
Sum equation:
Total number of questions can be given by =![x+y](https://tex.z-dn.net/?f=x%2By)
Total number of questions = 40
So, we have :
![x+y=40](https://tex.z-dn.net/?f=x%2By%3D40)
Points equation:
Total points for
number of 2 point question = ![2x](https://tex.z-dn.net/?f=2x)
Total points for
number of 4 point question = ![4y](https://tex.z-dn.net/?f=4y)
Total points in the test can be given by = ![2x+4y](https://tex.z-dn.net/?f=2x%2B4y)
Total points in the test = 100
So, we have :
![2x+4y=100](https://tex.z-dn.net/?f=2x%2B4y%3D100)
So, the system of equations is:
A) ![x+y=40](https://tex.z-dn.net/?f=x%2By%3D40)
B) ![2x+4y=100](https://tex.z-dn.net/?f=2x%2B4y%3D100)
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