Answer:
Number of true-false questions =15
Number of multiple choice questions =5
Step-by-step explanation:
Number of true-false questions =[tex]x[/tex]
Number of multiple choice questions =[tex]y[/tex]
Total number of question =[tex]x+y=20[/tex]
Points for true-false questions = 4
Total points for true-false questions = [tex]4\times x =4x[/tex]
Points for multiple choice questions = 8
Total points for multiple choice questions = [tex]8\times y =8y[/tex]
Total points of the test = [tex]4x+8y=100[/tex]
We have 2 equations now:
(1) [tex]x+y=20[/tex]
(2) [tex]4x+8y=100[/tex]
We need to solve the 2 equations to find [tex]x[/tex] and [tex]y[/tex].
Dividing equation 2 by 4.
[tex]\frac{4x+8y}{4}=\frac{100}{4}[/tex]
(2a) [tex]x+2y=25[/tex]
Multiplying equation (2a) with (-1)
[tex]-1(x+2y)=25\times (-1)[/tex]
(2b) [tex]-x-2y=-25[/tex]
Adding equation (2a) with equation (1).
[tex]x+y=20[/tex]
[tex]-x-2y=-25[/tex]
[tex]-y=-5[/tex]
[tex]y=5[/tex] [ Divided both sides by -1]
Substituting value of [tex]y[/tex] in equation (1).
[tex]x+5=20[/tex]
Subtracting both sides by 5.
[tex]x+5-5=20-5[/tex]
[tex]x=15[/tex]
∴[tex]x=15 \ and\ y=5[/tex]
Number of true-false questions =15
Number of multiple choice questions =5
