The average number of marbles that Bryan and Charlie have is 34.
The average number of marbles that Bryan and Adam have is 49.
The number of marbles that Charlie has is ²₅ as many as Adam.

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

(a)
Number of marbles that Bryan and Charlie has
= 2 x 34
= 68

Number of marbles that Bryan and Adam has
= 2 x 49
= 98

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

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


B + C = 68
B + 2 u = 68 --- (1)

B + A = 98
B + 5 u = 98 --- (2)

(2) - (1)
(B + 5 u) - (B + 2 u ) = 98 - 68
B + 5 u - B - 2 u = 30
B - B + 5 u - 2 u = 30

3 u = 30

1 u = 30 ÷ 3 = 10

Substitute 1 u = 10 into (1).
B + 2 x 10 = 68
B + 20 = 68
B = 68 - 20 = 48

Number of marbles that Bryan has = 48

(b)
Number of marbles that Charlie has
= 2 u
= 2 x 10
= 20

(c)
Number of marbles that Adam has
= 5 u
= 5 x 10
= 50

Answer(s): (a) 48; (b) 20; (c) 50