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

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:

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

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:

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

$40-2y+4y=50$

$40+2y=50$

$40-40+2y=50-40$

$2y=10$

$\frac{2y}{2}=\frac{10}{2}$

$y=5$

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.