The third column is in fact a red herring. It is not needed when finding the three colour-values. For example, examining the first two columns on the left, we can see immediately that black=red+5.
Armed with this information, we can then go to column four to calculate that red+red+red+(red+5)=45, which means that red must be 10. This leaves black as 15 and white as 2. The third column subsequently sums to 29.
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