Respuesta :
Answer:
15 two-point questions and 5 four-point questions.
Step-by-step explanation:
Let x represent number of two-points questions and y represent number of four-points questions.
We have been given that Janice wants to create a test containing 20 questions. We can represent this information in an equation as:
[tex]x+y=20...(1)[/tex]
Since all questions are worth 50 points. We can represent this information in an equation as:
[tex]2x+4y=50...(2)[/tex]
From equation (1), we will get:
[tex]x=20-y[/tex]
Upon substituting this value in equation (2), we will get:
[tex]2(20-y)+4y=50[/tex]
[tex]40-2y+4y=50[/tex]
[tex]40+2y=50[/tex]
[tex]40-40+2y=50-40[/tex]
[tex]2y=10[/tex]
[tex]\frac{2y}{2}=\frac{10}{2}[/tex]
[tex]y=5[/tex]
Therefore, there are 5 questions that are worth 4 points each.
Now, we will substitute [tex]y=5[/tex] in equation (1) to solve for x.
[tex]x+5=20[/tex]
[tex]x+5-5=20-5[/tex]
[tex]x=15[/tex]
Therefore, there are 15 questions that are worth 2 points each.
