The average number of marbles that Charlie and Bryan have is 37.
The average number of marbles that Charlie and Adam have is 51.
The number of marbles that Bryan has is ³₅ as many as Adam.

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

(a)
Number of marbles that Charlie and Bryan has
= 2 x 37
= 74

Number of marbles that Charlie and Adam has
= 2 x 51
= 102

Number of marbles that Bryan has = 3 u
Number of marbles that Adam has = 5 u

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


C + B = 74
C + 3 u = 74 --- (1)

C + A = 102
C + 5 u = 102 --- (2)

(2) - (1)
(C + 5 u) - (C + 3 u ) = 102 - 74
C + 5 u - C - 3 u = 28
C - C + 5 u - 3 u = 28

2 u = 28

1 u = 28 ÷ 2 = 14

Substitute 1 u = 14 into (1).
C + 3 x 14 = 74
C + 42 = 74
C = 74 - 42 = 32

Number of marbles that Charlie has = 32

(b)
Number of marbles that Bryan has
= 3 u
= 3 x 14
= 42

(c)
Number of marbles that Adam has
= 5 u
= 5 x 14
= 70

Answer(s): (a) 32; (b) 42; (c) 70