Answer:
The important variables in the problem are:
B. for multiple choice, for short answer
The number of multiple choice questions = 5
Step-by-step explanation:
Given:
Total number of questions = 15
Total points for the test = 60
Multiple choice question carries = 2 points
Short-answer question carries = 5 points
To determine the number of multiple choice questions in the test.
Solution:
Let represent the number of multiple choice questions.
If 1 multiple choice question carries = 2 points
The, questions will carry = points
Let represent the number of short-answer questions.
If 1 short-answe question carries = 5 points
The, questions will carry = points
Total questions can be given as :
Total points can be given as :
Thus, we can model two equations form the given data.
A) [Number of questions]
B) [ Total points]
Thus, and are important variables in the problem.
Rearranging equation A, to solve for in terms of
Subtracting both sides by
Substituting value of we got from A into equation B.
Using distribution.
Simplifying.
Subtracting both sides by 75.
Dividing both sides by -3.
∴
Thus, number of multiple choice questions = 5