Answer: The two point questions are 45, while the four point questions are 5.
Step-by-step explanation: We shall start by assigning letters to the unknown variables. Let the first type of question be called a and the second type of question be called b.
If the final exam is made up of 50 questions, that means
a + b = 50
Also if some questions are two points while others are four points and the total score for all of them is 110 points, then
2a + 4b = 110
(That is, we assume that a is the two point question and b is the four point question, so total score equals 110)
We now have a pair of simultaneous equations
a + b = 50 ————(1)
2a + 4b = 110 ——-(2)
From equation (1), we shall make a the subject of the equation,
hence let a = 50 - b
Substitute for the value of a in equation (2)
2a + 4b = 110
2(50 - b) + 4b = 110
100 - 2b + 4b = 110
By collecting like terms we now have
4b - 2b = 110 - 100
2b = 10
Divide both sides of the equation by 2
b = 5
Now substitute for the value of b into equation (1)
a + b = 50
a + 5 = 50
Subtract 5 from both sides of the equation
a = 45.
Therefore the two point questions are 45, while the four point questions are 5
**A quick check would show the following results ; 2(45) + 4(5) = 90 + 20 = 110.**
