Riddles, brain puzzles and mathematical problems

[Wapez]

Spoiler below!

acb = abc + 9:

100a + 10c + b = 100a + 10 b + c + 9 <=>
10c + b = 10b + c + 9 <=>
9c = 9b + 9 <=>
c = b + 1 <=>
b = c - 1 (1)


bac = abc + 90:
100b + 10 a + c = 100a + 10 b + c + 90 <=>
90b = 90a + 90 <=>
b = a + 1 (2)

(1),(2) => c-1 = a+1 <=>
c-a = 2(3)



cba = 100c + 10b + a = 100a +10b + c - 99a + 99c =
100a + 10b + c + 99(c-a) = with (3)
= 100a + 10b + c + 198

cba = abc + 198

(I hope I haven't made any stupid mistake here)

Well done, correct!

Please spoiler it though, so other people have the same chance.