The average number of marbles that Adam and Charlie have is 7.
The average number of marbles that Charlie and Bryan have is 5.
The average number of marbles that Bryan and Adam have is 6.
- How many marbles does Adam have?
- How many marbles does Charlie have?
- How many marbles does Bryan have?
(a)
Let the number of marbles that Adam has be A.
Let the number of marbles that Charlie has be C.
Let the number of marbles that Bryan has be B.
A + C = 2 x 7 = 14 --- (1)
C + B = 2 x 5 = 10 --- (2)
A + B = 2 x 6 = 12 --- (3)
(A + C) + (C + B) + (A + B) = 14 + 10 + 12
2 x (A + C + B) = 36
A + C + B = 36 ÷ 2
A + C + B = 18 --- (4)
Substitute (2) into (4).
A + C + B = 18
A + 10 = 18
A = 18 - 10 = 8
Number of marbles that Adam has = 8
(b)
Substitute A = 8 into (1).
A + C = 14
8 + C = 14
C = 14 - 8 = 6
Number of marbles that Charlie has = 6
(c)
Substitute Charlie's marbles = 6 into (2).
C + B = 10
6 + B = 10
B = 10 - 6 = 4
Number of marbles that Bryan has = 4
Answer(s): (a) 8; (b) 6; (c) 4