The average number of beads that Bryan and Charlie have is 6.
The average number of beads that Charlie and Adam have is 5.
The average number of beads that Adam and Bryan have is 9.

1. How many beads does Bryan have?
2. How many beads does Charlie have?
3. How many beads does Adam have?

(a)
Let the number of beads that Bryan has be B.
Let the number of beads that Charlie has be C.
Let the number of beads that Adam has be A.

B + C = 2 x 6 = 12 --- (1)
C + A = 2 x 5 = 10 --- (2)
B + A = 2 x 9 = 18 --- (3)

(B + C) + (C + A) + (B + A) = 12 + 10 + 18
2 x (B + C + A) = 40
B + C + A = 40 ÷ 2
B + C + A = 20 --- (4)

Substitute (2) into (4).
B + C + A = 20
B + 10 = 20

B = 20 - 10 = 10

Number of beads that Bryan has = 10

(b)
Substitute B = 10 into (1).
B + C = 12
10 + C = 12 

C = 12 - 10 = 2

Number of beads that Charlie has = 2

(c)
Substitute Charlie's beads = 2 into (2).
C + A = 10
2 + A = 10

A = 10 - 2 = 8

Number of beads that Adam has = 8

Answer(s): (a) 10; (b) 2; (c) 8