beads on table

There are twice as many green beads as blue beads and the number of red beads is seven more than half the total number of green and blue beads. Given that I do not have more than 50 beads, what’s the MAX possible number of blue beads that I could have?

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.