Number of Blue = b
Number of Green = g = 2b
Number of Red = r = (3b/2) + 7
Total beads = b + 2b + (3b/2) + 7 = (9b/2) +7
9b/2 is not greater than 43 (50-7), because the red beads are seven more than everything.
Maximum value for b (including partial beads) = 43/(9b/2) = 86/9 = 9.556 (approx.)
As we can’t have part beads, max blue beads = 9, but an odd value for b would give a partial bead of red, so maximum number of blue beads = 8
Answer: 8 blue beads
Double check 8 + (2 X 8) + (3 X 8/2) + 7 = 8 + 16 + 12 + 7 = 43
Thank you, Nigel Parsons, Quora contributor, puzzler, gamer, sci-fi nut.