<p>I agree with setzwxman - if you can do without equations (and I do like tackling them!), then do it. In many cases it's faster and more error proof, because you see everything clearly, not just some abstract constructions.
I would use setzwxman's approach with one change. It's easier to work with whole numbers, so in questions on mixes/parts choose LCD of total parts, then ingredients will be integers too.</p>
<p>Orange mix - 5 parts (R3+Y2)
Green mix - 3 parts (B2+Y1).
IMPORTANT: please note that parts in Orange and Green mixes are not assumed to be the same, even though they can.
For example, if we had 10L of Orange and 6L of Green, each part in both would be 2L.
Anyway, LCD(5,3)=15. If we have 15L of each mix, then
== in Orange one part is (15/5)L = 3L.
and there are 3L * 2 = 6L of Yellow stuff in it;
== in Green one part is (15/3)L = 5L
and that's exactly how much of Yellow dye is in it.
Joining equal amounts 15L of each Orange and Green we get 30L of new mix.
There are 6L + 5L = 11L of Yellow dye in it.
11 out of 30 is 11/30 - the answer.
++++++
Just out of curiosity:
from Orange come (15/5)L * 3 = 9L of Red
from Green come (15/3)L * 2 = 10L of Blue.
So in 30L of a final mix there'll be
11L of Yellow
9L of Red
10L of Blue.
Their ratio is 11:9:10.
We are ready to answer any possible question on this mix.</p>
<h1>What's the ratio Yellow to Blue, or (Yellow and Blue) to Red, etc.</h1>
<p>Question to artists:
is this new dye of any particular color?</p>