The average number of beads that Adam and Charlie have is 35.
The average number of beads that Adam and Bryan have is 57.
The number of beads that Charlie has is ³₅ as many as Bryan.

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

(a)
Number of beads that Adam and Charlie has
= 2 x 35
= 70

Number of beads that Adam and Bryan has
= 2 x 57
= 114

Number of beads that Charlie has = 3 u
Number of beads that Bryan has = 5 u

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


A + C = 70
A + 3 u = 70 --- (1)

A + B = 114
A + 5 u = 114 --- (2)

(2) - (1)
(A + 5 u) - (A + 3 u ) = 114 - 70
A + 5 u - A - 3 u = 44
A - A + 5 u - 3 u = 44

2 u = 44

1 u = 44 ÷ 2 = 22

Substitute 1 u = 22 into (1).
A + 3 x 22 = 70
A + 66 = 70
A = 70 - 66 = 4

Number of beads that Adam has = 4

(b)
Number of beads that Charlie has
= 3 u
= 3 x 22
= 66

(c)
Number of beads that Bryan has
= 5 u
= 5 x 22
= 110

Answer(s): (a) 4; (b) 66; (c) 110