A quiz had some 3-point and some 4-point questions. A perfect score was 100 points. Find out how many questions were of each type if there were a total of 31 questions on the quiz

I have no clue how to start this.

X 3-pt questions.

(31-x) 4-pt question.

3x + 4(31-x) = 100 Points.
3x + 124 -4x = 100
-x = 100-124 = -24

X = 24. 3-pt questions.
(31-x) = 31-24 = 7 4-pt questions.

To solve this problem, let's start by assigning variables to the unknown quantities that we're trying to find. Let's call the number of 3-point questions "x" and the number of 4-point questions "y". We need to find the values of x and y.

We can set up two equations based on the given information:

1. x + y = 31 (since there were a total of 31 questions on the quiz)
2. 3x + 4y = 100 (since a perfect score was 100 points)

Now we have a system of two equations with two unknowns. We can solve this system of equations by using either the substitution method or the elimination method.

Let's use the substitution method to solve this system:

From equation 1, we can express x in terms of y:
x = 31 - y

Substitute this value of x into equation 2:
3(31 - y) + 4y = 100
93 - 3y + 4y = 100
93 + y = 100
y = 100 - 93
y = 7

Now substitute the value of y back into equation 1 to find the value of x:
x + 7 = 31
x = 31 - 7
x = 24

Therefore, there were 24 3-point questions and 7 4-point questions on the quiz.