The average number of beads that Charlie and Adam have is 9.
The average number of beads that Adam and Bryan have is 7.
The average number of beads that Bryan and Charlie have is 8.
- How many beads does Charlie have?
- How many beads does Adam have?
- How many beads does Bryan have?
(a)
Let the number of beads that Charlie has be C.
Let the number of beads that Adam has be A.
Let the number of beads that Bryan has be B.
C + A = 2 x 9 = 18 --- (1)
A + B = 2 x 7 = 14 --- (2)
C + B = 2 x 8 = 16 --- (3)
(C + A) + (A + B) + (C + B) = 18 + 14 + 16
2 x (C + A + B) = 48
C + A + B = 48 ÷ 2
C + A + B = 24 --- (4)
Substitute (2) into (4).
C + A + B = 24
C + 14 = 24
C = 24 - 14 = 10
Number of beads that Charlie has = 10
(b)
Substitute C = 10 into (1).
C + A = 18
10 + A = 18
A = 18 - 10 = 8
Number of beads that Adam has = 8
(c)
Substitute Adam's beads = 8 into (2).
A + B = 14
8 + B = 14
B = 14 - 8 = 6
Number of beads that Bryan has = 6
Answer(s): (a) 10; (b) 8; (c) 6