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

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

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

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

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

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

C = 20 - 10 = 10

Number of beads that Charlie has = 10

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

B = 12 - 10 = 2

Number of beads that Bryan has = 2

(c)
Substitute Bryan's beads = 2 into (2).
B + A = 10
2 + A = 10

A = 10 - 2 = 8

Number of beads that Adam has = 8

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