white : milk : dark
w : m : d
The ratio of white to not white is 3:4
w : (m+d) = 3:4
The ratio of not dark to dark is 17:4.
(w+m) : d = 17:4
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We treat the colons as fraction bars and cross multiply.
4w = 3(m+d) = 3m + 3d
4w + 4m = 17 d
Subtracting,
4m = 17d - (3m+3d) = 14d - 3m
7m = 14 d
m/d = 14/7
m:d = 2:1
Since w:(m+d)=3:4 let's make m+d a multiple of 4.
m:d = 8:4
w : (m+d) = 3:4 = 9:12
w:m:d = 9:8:4
Answer: 9:8:4
Check:
white to non white 9 to 8+4=12 = 3:4, good
non dark to dark (9+8):4=17:4, good
