Respuesta :
Answer:
The important variables in the problem are:
B. [tex]m[/tex] for multiple choice, [tex]s[/tex] 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 [tex]m[/tex] represent the number of multiple choice questions.
If 1 multiple choice question carries = 2 points
The, [tex]m[/tex] questions will carry = [tex]2m[/tex] points
Let [tex]s[/tex] represent the number of short-answer questions.
If 1 short-answe question carries = 5 points
The, [tex]s[/tex] questions will carry = [tex]5s[/tex] points
Total questions can be given as :
[tex]m+s[/tex]
Total points can be given as :
[tex]2m+5s[/tex]
Thus, we can model two equations form the given data.
A) [tex]m+s=15[/tex] [Number of questions]
B) [tex]2m+5s=60[/tex] [ Total points]
Thus, [tex]m[/tex] and [tex]s[/tex] are important variables in the problem.
Rearranging equation A, to solve for [tex]s[/tex] in terms of [tex]m[/tex]
Subtracting both sides by [tex]m[/tex]
[tex]m+s-m=15-m[/tex]
[tex]s=15-m[/tex]
Substituting value of [tex]s[/tex] we got from A into equation B.
[tex]2m+5(15-m)=60[/tex]
Using distribution.
[tex]2m+75-5m=60[/tex]
Simplifying.
[tex]-3m+75=60[/tex]
Subtracting both sides by 75.
[tex]-3m+75-75=60-75[/tex]
[tex]-3m=-15[/tex]
Dividing both sides by -3.
[tex]\frac{-3m}{-3}=\frac{-15}{-3}[/tex]
∴ [tex]m=5[/tex]
Thus, number of multiple choice questions = 5
