The average number of beads that Adam and Bryan have is 32.
The average number of beads that Adam and Charlie have is 46.
The number of beads that Bryan has is ⁵₉ as many as Charlie.

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

(a)
Number of beads that Adam and Bryan has
= 2 x 32
= 64

Number of beads that Adam and Charlie has
= 2 x 46
= 92

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

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


A + B = 64
A + 5 u = 64 --- (1)

A + C = 92
A + 9 u = 92 --- (2)

(2) - (1)
(A + 9 u) - (A + 5 u ) = 92 - 64
A + 9 u - A - 5 u = 28
A - A + 9 u - 5 u = 28

4 u = 28

1 u = 28 ÷ 4 = 7

Substitute 1 u = 7 into (1).
A + 5 x 7 = 64
A + 35 = 64
A = 64 - 35 = 29

Number of beads that Adam has = 29

(b)
Number of beads that Bryan has
= 5 u
= 5 x 7
= 35

(c)
Number of beads that Charlie has
= 9 u
= 9 x 7
= 63

Answer(s): (a) 29; (b) 35; (c) 63