Question

Janice wants to create a test containing 20 questions worth 50 points. If Janice creates questions worth either two points or four points, she can include (blank)

two-point questions and (blank) four-point questions.

Answer 1

15 two-point questions and 5 four-point questions.

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:

`x+y=20...(1)`

Since all questions are worth 50 points. We can represent this information in an equation as:

`2x+4y=50...(2)`

From equation (1), we will get:

`x=20-y`

Upon substituting this value in equation (2), we will get:

`2(20-y)+4y=50`

`40-2y+4y=50`

`40+2y=50`

`40-40+2y=50-40`

`2y=10`

`(2y)/(2)=(10)/(2)`

`y=5`

Therefore, there are 5 questions that are worth 4 points each.

Now, we will substitute
`y=5` in equation (1) to solve for x.

`x+5=20`

`x+5-5=20-5`

`x=15`

Therefore, there are 15 questions that are worth 2 points each.