Answer:
9/11
Step-by-step explanation:
Let r = number of red gems
Let n = number of green gems
Let p = number of gold gems
n= (1/3)r   - - >   multiply both sides by 3  - - >   r = 3n
r = (1/6)p  - - >   multiply both sides by 6  - - >  p = 6r
So the number of reds (r) is 3x the number of greens (n)
And the number of golds (p) is 6x the number of reds.
So for every 1 green, we have 3 reds and for every red we have 6 golds.
So for every 1 green, we have 3 reds and 18 golds. 
So we add 1 + 3 + 18 = 22 gems.
Out of the 22 gems, 18 are gold.
18/22 = 9/11 are gold