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 :
![m+s](https://tex.z-dn.net/?f=m%2Bs)
Total points can be given as :
![2m+5s](https://tex.z-dn.net/?f=2m%2B5s)
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