The average number of marbles that Adam and Bryan have is 38.
The average number of marbles that Adam and Charlie have is 56.
The number of marbles that Bryan has is ²₅ as many as Charlie.

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

(a)
Number of marbles that Adam and Bryan has
= 2 x 38
= 76

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

Number of marbles that Bryan has = 2 u
Number of marbles that Charlie has = 5 u

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


A + B = 76
A + 2 u = 76 --- (1)

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

(2) - (1)
(A + 5 u) - (A + 2 u ) = 112 - 76
A + 5 u - A - 2 u = 36
A - A + 5 u - 2 u = 36

3 u = 36

1 u = 36 ÷ 3 = 12

Substitute 1 u = 12 into (1).
A + 2 x 12 = 76
A + 24 = 76
A = 76 - 24 = 52

Number of marbles that Adam has = 52

(b)
Number of marbles that Bryan has
= 2 u
= 2 x 12
= 24

(c)
Number of marbles that Charlie has
= 5 u
= 5 x 12
= 60

Answer(s): (a) 52; (b) 24; (c) 60