The average number of marbles that Adam and Bryan have is 3.
The average number of marbles that Bryan and Charlie have is 4.
The average number of marbles that Charlie and Adam have is 5.
- How many marbles does Adam have?
- How many marbles does Bryan have?
- How many marbles does Charlie have?
(a)
Let the number of marbles that Adam has be A.
Let the number of marbles that Bryan has be B.
Let the number of marbles that Charlie has be C.
A + B = 2 x 3 = 6 --- (1)
B + C = 2 x 4 = 8 --- (2)
A + C = 2 x 5 = 10 --- (3)
(A + B) + (B + C) + (A + C) = 6 + 8 + 10
2 x (A + B + C) = 24
A + B + C = 24 ÷ 2
A + B + C = 12 --- (4)
Substitute (2) into (4).
A + B + C = 12
A + 8 = 12
A = 12 - 8 = 4
Number of marbles that Adam has = 4
(b)
Substitute A = 4 into (1).
A + B = 6
4 + B = 6
B = 6 - 4 = 2
Number of marbles that Bryan has = 2
(c)
Substitute Bryan's marbles = 2 into (2).
B + C = 8
2 + C = 8
C = 8 - 2 = 6
Number of marbles that Charlie has = 6
Answer(s): (a) 4; (b) 2; (c) 6