The average number of stickers that Charlie and Adam have is 6.
The average number of stickers that Adam and Bryan have is 7.
The average number of stickers that Bryan and Charlie have is 9.
- How many stickers does Charlie have?
- How many stickers does Adam have?
- How many stickers does Bryan have?
(a)
Let the number of stickers that Charlie has be C.
Let the number of stickers that Adam has be A.
Let the number of stickers that Bryan has be B.
C + A = 2 x 6 = 12 --- (1)
A + B = 2 x 7 = 14 --- (2)
C + B = 2 x 9 = 18 --- (3)
(C + A) + (A + B) + (C + B) = 12 + 14 + 18
2 x (C + A + B) = 44
C + A + B = 44 ÷ 2
C + A + B = 22 --- (4)
Substitute (2) into (4).
C + A + B = 22
C + 14 = 22
C = 22 - 14 = 8
Number of stickers that Charlie has = 8
(b)
Substitute C = 8 into (1).
C + A = 12
8 + A = 12
A = 12 - 8 = 4
Number of stickers that Adam has = 4
(c)
Substitute Adam's stickers = 4 into (2).
A + B = 14
4 + B = 14
B = 14 - 4 = 10
Number of stickers that Bryan has = 10
Answer(s): (a) 8; (b) 4; (c) 10