The average number of marbles that Adam and Charlie have is 39.
The average number of marbles that Adam and Bryan have is 56.
The number of marbles that Charlie has is ³₅ as many as Bryan.

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

(a)
Number of marbles that Adam and Charlie has
= 2 x 39
= 78

Number of marbles that Adam and Bryan has
= 2 x 56
= 112

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

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


A + C = 78
A + 3 u = 78 --- (1)

A + B = 112
A + 5 u = 112 --- (2)

(2) - (1)
(A + 5 u) - (A + 3 u ) = 112 - 78
A + 5 u - A - 3 u = 34
A - A + 5 u - 3 u = 34

2 u = 34

1 u = 34 ÷ 2 = 17

Substitute 1 u = 17 into (1).
A + 3 x 17 = 78
A + 51 = 78
A = 78 - 51 = 27

Number of marbles that Adam has = 27

(b)
Number of marbles that Charlie has
= 3 u
= 3 x 17
= 51

(c)
Number of marbles that Bryan has
= 5 u
= 5 x 17
= 85

Answer(s): (a) 27; (b) 51; (c) 85