An instructor wants to write a test with 25 questions where each question is worth 3, 4, or 5 points based on difficulty. he wants the number of 3-point questions to be 4 less than the number of 4-point questions, and he wants the quiz to be worth a total of 100 points. how many 3, 4, and 5 point questions are there?

3-point questions = 7

4-point questions = 11

5-point questions = 7

Step-by-step explanation:

Let x, y and z be number of 3-point, 4-point and 5-point questions respectively.

We are told that number of total questions in the quiz is 25.

We are also told that number of 3-point questions is 4 less than the number of 4-point questions.

The quiz is worth 100 points.

Substituting equation 2 in equation 1 we will get,

Upon substituting value of y and z in equation 3 we will get,

Therefore, number of 3-point questions is 7.

Now we will find y by substituting x=7 in equation 2.

Therefore, number of 4-point questions will be 11.

Now we will substitute value of x and y in equation 1 to find our z.

Therefore, number of 5-point questions is 7.  

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