Box H contains 2 gold beads and 11 black beads. Box J contains 39 gold beads and 12 black beads. How many black beads and gold beads must be transferred from Box J to put into Box H so that 50% of the beads in Box A are gold and 75% of the beads in Box J are gold?

	Box H		Box J
	Gold beads	Black beads	Gold beads	Black beads
Before	2	11	39	12
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of gold beads = 2 + 39 = 41 

Number of black beads = 11 + 12 = 23 

1 u + 3 p = 41 --- (1)

1 u + 1 p = 23 ---(2)

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 41 - 23
3 p - 1 p = 18
2 p = 18

1 p = 18 ÷ 2 = 9

From (2):
1 u + 1 p = 23
1 u + 1 x 9 = 23
1 u + 9 = 23

1 u = 23 - 9 = 14

Number of black beads to be transferred from Box J to Box H
= 12 - 1 p
= 12 - 1 x 9
= 12 - 9
= 3

Number of gold beads to be transferred from Box J to Box H
= 1 u - 2
= 14 - 2
= 12

Total number of black and gold beads to be transferred from Box J to Box H
= 3 + 12
= 15

Answer(s): 15