Box G contains 4 brown marbles and 12 purple marbles. Box H contains 49 brown marbles and 15 purple marbles. How many purple marbles and brown marbles must be removed from Box H to put into Box G so that 50% of the marbles in Box A are brown and 75% of the marbles in Box H are brown?

	Box G		Box H
	Brown marbles	Purple marbles	Brown marbles	Purple marbles
Before	4	12	49	15
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of brown marbles = 4 + 49 = 53 

Number of purple marbles = 12 + 15 = 27 

1 u + 3 p = 53 --- (1)

1 u + 1 p = 27 ---(2)

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 53 - 27
3 p - 1 p = 26
2 p = 26

1 p = 26 ÷ 2 = 13

From (2):
1 u + 1 p = 27
1 u + 1 x 13 = 27
1 u + 13 = 27

1 u = 27 - 13 = 14

Number of purple marbles to be removed from Box H to Box G
= 15 - 1 p
= 15 - 1 x 13
= 15 - 13
= 2

Number of brown marbles to be removed from Box H to Box G
= 1 u - 4
= 14 - 4
= 10

Total number of purple and brown marbles to be removed from Box H to Box G
= 2 + 10
= 12

Answer(s): 12