Respuesta :
Answer:
Number of 2-point questions = 30
Number of 4-point questions = 10
Step-by-step explanation:
Let the number of 2 point questions = [tex]x[/tex]
Let the number of 4 point questions = [tex]y[/tex]
Sum equation:
Total number of questions can be given by =[tex]x+y[/tex]
Total number of questions = 40
So, we have :
[tex]x+y=40[/tex]
Points equation:
Total points for [tex]x[/tex] number of 2 point question = [tex]2x[/tex]
Total points for [tex]y[/tex] number of 4 point question = [tex]4y[/tex]
Total points in the test can be given by = [tex]2x+4y[/tex]
Total points in the test = 100
So, we have :
[tex]2x+4y=100[/tex]
So, the system of equations is:
A) [tex]x+y=40[/tex]
B) [tex]2x+4y=100[/tex]
Rearranging equation A, to solve for [tex]y[/tex] in terms of [tex]x[/tex]
Subtracting both sides by [tex]x[/tex]
[tex]x+y-x=40-x[/tex]
[tex]y=40-x[/tex]
Substituting value of [tex]y[/tex] we got from A into equation B.
[tex]2x+4(40-x)=100[/tex]
Using distribution.
[tex]2x+160-4x=100[/tex]
Simplifying.
[tex]-2x+160=100[/tex]
Subtracting both sides by 160.
[tex]-2x+160-160=100-160[/tex]
[tex]-2x=-60[/tex]
Dividing both sides by -2.
[tex]\frac{-2x}{-2}=\frac{-60}{-2}[/tex]
[tex]x=30[/tex]
We can plugin [tex]x=30[/tex] in the rearranged equation A to get value of [tex]y[/tex]
[tex]y=40-30[/tex]
∴[tex]y=10[/tex]
Thus, number of 2-point questions = 30
Number of 4-point questions = 10
