1. There are x 3-point questions, and y 5-point questions.
In total there are 24 questions mean : x+y=24,
In total there are 100 points, so x*3 (x questions each 3 points of worth)+y*5 (y questions each 5 point of worth) make a total of 100 points.
The situation is described by the system:
(i) x+y=24
(ii) 3x+5y=100
from x+y=24, we can write y=24-x
substitute in (ii):
3x+5(24-x)=100
3x+5*24-5*x=100
3x+120-5x=100
3x-5x=100-120
-2x=-20
x=-20/(-2)=10
from this, y=24-x=24-10=12
Answer: The test contains 10 three-point questions and 14 five-point questions.
