Let P2 is the problem that is worth 2 points and P5 the problem that is worth 5 points
we will have: P2 + P5 = 38 (1) we will also have: 2P2 + 5P5 = 100 (2)
from the (1) we get P2 = 38 - P5 substituting on (2) where P2 = 38 - P5 we get 2(38 - P5) + 5P5 = 100
->> 76 - 2P5 + 5P5 = 100 ->> 3P5 = 100 - 76 ->> 3P5 = 24 ->> P5 = 24/3 = 8 so the 5 points problems
are 8 substituting to (1) where P5 = 8 we get P2 = 38 - P5 ->> P2 = 38 - 8 = 30 So the 2 points problems
are 30
So we will have 8 * 5 = 40 and. 30 * 2 = 60 so total problems 40 + 60 = 100