A 110 point final exam is
made up of 50 questions.
Some questions are worth 2
points and some are worth
4 points. How many of
each type of question are
on the test?

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.**