The average number of beads that Charlie and Bryan have is 34.
The average number of beads that Charlie and Adam have is 54.
The number of beads that Bryan has is ⁵₉ as many as Adam.

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

(a)
Number of beads that Charlie and Bryan has
= 2 x 34
= 68

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

Number of beads that Bryan has = 5 u
Number of beads that Adam has = 9 u

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


C + B = 68
C + 5 u = 68 --- (1)

C + A = 108
C + 9 u = 108 --- (2)

(2) - (1)
(C + 9 u) - (C + 5 u ) = 108 - 68
C + 9 u - C - 5 u = 40
C - C + 9 u - 5 u = 40

4 u = 40

1 u = 40 ÷ 4 = 10

Substitute 1 u = 10 into (1).
C + 5 x 10 = 68
C + 50 = 68
C = 68 - 50 = 18

Number of beads that Charlie has = 18

(b)
Number of beads that Bryan has
= 5 u
= 5 x 10
= 50

(c)
Number of beads that Adam has
= 9 u
= 9 x 10
= 90

Answer(s): (a) 18; (b) 50; (c) 90