Hi Wayne,

7/12 would be for one case.

What if there are other possibilities?

Like so:

Given away:
5/12 R
1/3 B
7/9 G

*Green marbles that were Given away is 2/3 of total given away

Qn: What is the fraction given away?

Possible numbers of marbles given away:

G: 14, 28, 42,...
(Note: not possible to give odd number of green marbles, if not it will not be 2/3 of the marbles given away)
B: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,...16,...
R: 5, 10, 15, 20, 25, 30,...

Assume 14 marbles given away (Lowest multiple of 7 which is also a multiple of 2)
14*1/2=7 (R and B) given away
14*3/2=21 (R and B and G) given away

5 red given away)
2 blue given away)
(Lowest numbers of red and blue to give 7)

Fraction given away = 21/total

Total = 14*9/7+ 12/5*5 + 3*2 = 36
21/36= 7/12


***One possible combination
Colour; Total; (Given Away)
R 12 (5)
B 6 (2)
G 18 (14)

21/36=7/12

Another possible combination:
R 24 (10)
B 12 (4)
G 36 (28)
42/72=7/12

If (R+B given away)= 14 (10+4) or (5+9)

However, another combination is:
R 12 (5)
B 27 (9)
G 36 (28)
* 42/75= 14/25 but not equal to 7/12

Another possible combination:
R 36 (15)
B 18(6)
G 54 (42)
* 63/105=7/12


Still another combination is:

R 12(5)
B 48 (16)
G 54 (42)
* 63/114=21/38 but not equal to 7/12

3 different fraction answers.

Possible there is an error in the question?