An instructor wants to make a question paper of 25 marks with 8 questions where each
question is worth 2, 3, or 5 marks based on difficulty. He wants the number of 2-mark
questions to be 1 more than the number of 5-mark questions. How many 2, 3, and 5
mark questions could be there?
Answers
Answer:
............................................
-1, 9, 0 many questions with 2, 3, and 5 marks are possible when teacher wishes to create a 25 mark exam with 8 questions
Given that,
A teacher wishes to create a 25 mark exam with 8 questions, each worth 2, 3, or 5 marks depending on how difficult they are. He desires that there be one more 2-mark questions than 5-mark questions.
We have to find how many questions with 2, 3, and 5 marks are possible.
We know that,
Let x, y, and z represent the number of questions with two marks, three marks, and five marks, respectively.
It states that there are eight questions in all.
So we have:
x + y + z = 8 ---------->equation(1)
The total amount of marks is 25, with each question worth 2, 3, or 5.
2x+3y+5z=25 ---------->equation(2)
z = x+1
Equation (1) and (2) will be
x + y + x +1 =8
2x + y = 7 --------->equation(3)
2x + 3y + 5x + 5 = 25
7x + 3y = 20 --------->equation(4)
Subtracting 3 and 4 equation
x =-1
z = -1+1 = 0
-2 + y = 7
y = 7+2
y = 9
Therefore, -1, 9, 0 many questions with 2, 3, and 5 marks are possible.
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