Here are two made-up operations, g and r.
If 10 g = 16, 100 g = 196, and 4 g = 4; and also if 12 r = 5, 300 r = 101, 30 r = 11,
then what is n if n g r = 9?
(Notation: n g r means we do g to n and then r to that. So n g r means (ng)r .)
Solution
g: 10 \rightarrow 16 ,  100 \rightarrow 196 ,  4 \rightarrow 4 ,   x \rightarrow 2x – 4
r: 12 \rightarrow 5 ,  300 \rightarrow 101 ,  30 \rightarrow 11 ,  x \rightarrow x/3 + 1
g r: n (2n - 4)/3 + 1 = 9
(2n – 4)/3 + 1 = 9
2n – 4 = 24
n = 14
Check: 14 g r = (2*14 – 4)/3 + 1 = 24/3 + 1 = 9