Changing the incorrect number 49 for 63 then...
63 x 1/9 x W + 82 x 1/12 x (552 - W))
so you can simplify the 63 with the 9 and the 82 with the 12
7 x W + 7 x (552 - W)
Actually at the end you have just to multiply 7x552 and you get the number
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Yeah I get it now. Your approach is just unnecessarily complicated.
It's kinda weird, but I made some mistake in thinking that different number pairs would lead to different solutions. Ofcourse they are both divided by 7 eventually, which I missed at 49 and therefore thought the same would be true at 63.