Container H contains 2 grey beads and 6 black beads. Container J contains 71 grey beads and 31 black beads. How many black beads and grey beads must be moved from Container J to put into Container H so that 50% of the beads in Container A are grey and 75% of the beads in Container J are grey?

	Container H		Container J
	Grey beads	Black beads	Grey beads	Black beads
Before	2	6	71	31
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of grey beads = 2 + 71 = 73 

Number of black beads = 6 + 31 = 37 

1 u + 3 p = 73 --- (1)

1 u + 1 p = 37 ---(2)

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 73 - 37
3 p - 1 p = 36
2 p = 36

1 p = 36 ÷ 2 = 18

From (2):
1 u + 1 p = 37
1 u + 1 x 18 = 37
1 u + 18 = 37

1 u = 37 - 18 = 19

Number of black beads to be moved from Container J to Container H
= 31 - 1 p
= 31 - 1 x 18
= 31 - 18
= 13

Number of grey beads to be moved from Container J to Container H
= 1 u - 2
= 19 - 2
= 17

Total number of black and grey beads to be moved from Container J to Container H
= 13 + 17
= 30

Answer(s): 30