The average number of marbles that Bryan and Adam have is 6.
The average number of marbles that Adam and Charlie have is 7.
The average number of marbles that Charlie and Bryan have is 5.

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

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

B + A = 2 x 6 = 12 --- (1)
A + C = 2 x 7 = 14 --- (2)
B + C = 2 x 5 = 10 --- (3)

(B + A) + (A + C) + (B + C) = 12 + 14 + 10
2 x (B + A + C) = 36
B + A + C = 36 ÷ 2
B + A + C = 18 --- (4)

Substitute (2) into (4).
B + A + C = 18
B + 14 = 18

B = 18 - 14 = 4

Number of marbles that Bryan has = 4

(b)
Substitute B = 4 into (1).
B + A = 12
4 + A = 12 

A = 12 - 4 = 8

Number of marbles that Adam has = 8

(c)
Substitute Adam's marbles = 8 into (2).
A + C = 14
8 + C = 14

C = 14 - 8 = 6

Number of marbles that Charlie has = 6

Answer(s): (a) 4; (b) 8; (c) 6