If Janice creates questions worth either two points or four points, how many four point questions does she need?

Question

Janice wants to create a test with 20 question worth 50 points.

Answer 1

Here's what we know:

t + f = 20 (there are a total of 20 questions)

2t + 4f = 50 (two- and four-point quest ions make 50 points)

 

Let's use elimination to solve. Multiply the first equation by -2:

-2t - 2f = -40

2t + 4f = 50

-----------------

2f = 10

Divide by 2:

f = 5

 

t + 5 = 20

t = 15

 

check:

2 * 15 + 4 * 5 = 50

30 + 20 = 50

50 = 50