Sort:  

Yes correct!

Would you mind explaining why that's the answer?

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

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.

then the riddle is unsolvable