The average number of beads that Charlie and Adam have is 27.
The average number of beads that Charlie and Bryan have is 54.
The number of beads that Adam has is ²₅ as many as Bryan.

1. How many beads does Charlie have?
2. How many beads does Adam have?
3. How many beads does Bryan have?

(a)
Number of beads that Charlie and Adam has
= 2 x 27
= 54

Number of beads that Charlie and Bryan has
= 2 x 54
= 108

Number of beads that Adam has = 2 u
Number of beads that Bryan has = 5 u

Let the number of Charlie's beads be C.
Let the number of Adam's beads be A.
Let the number of Bryan's beads be B.


C + A = 54
C + 2 u = 54 --- (1)

C + B = 108
C + 5 u = 108 --- (2)

(2) - (1)
(C + 5 u) - (C + 2 u ) = 108 - 54
C + 5 u - C - 2 u = 54
C - C + 5 u - 2 u = 54

3 u = 54

1 u = 54 ÷ 3 = 18

Substitute 1 u = 18 into (1).
C + 2 x 18 = 54
C + 36 = 54
C = 54 - 36 = 18

Number of beads that Charlie has = 18

(b)
Number of beads that Adam has
= 2 u
= 2 x 18
= 36

(c)
Number of beads that Bryan has
= 5 u
= 5 x 18
= 90

Answer(s): (a) 18; (b) 36; (c) 90