The average number of marbles that Bryan and Charlie have is 6.
The average number of marbles that Charlie and Adam have is 3.
The average number of marbles that Adam and Bryan have is 5.
- How many marbles does Bryan have?
- How many marbles does Charlie have?
- How many marbles does Adam have?
(a)
Let the number of marbles that Bryan has be B.
Let the number of marbles that Charlie has be C.
Let the number of marbles that Adam has be A.
B + C = 2 x 6 = 12 --- (1)
C + A = 2 x 3 = 6 --- (2)
B + A = 2 x 5 = 10 --- (3)
(B + C) + (C + A) + (B + A) = 12 + 6 + 10
2 x (B + C + A) = 28
B + C + A = 28 ÷ 2
B + C + A = 14 --- (4)
Substitute (2) into (4).
B + C + A = 14
B + 6 = 14
B = 14 - 6 = 8
Number of marbles that Bryan has = 8
(b)
Substitute B = 8 into (1).
B + C = 12
8 + C = 12
C = 12 - 8 = 4
Number of marbles that Charlie has = 4
(c)
Substitute Charlie's marbles = 4 into (2).
C + A = 6
4 + A = 6
A = 6 - 4 = 2
Number of marbles that Adam has = 2
Answer(s): (a) 8; (b) 4; (c) 2