Container U contains 11 black marbles and 12 purple marbles. Container V contains 18 black marbles and 7 purple marbles. How many purple marbles and black marbles must be removed from Container V to put into Container U so that 50% of the marbles in Container A are black and 75% of the marbles in Container V are black?

	Container U		Container V
	Black marbles	Purple marbles	Black marbles	Purple marbles
Before	11	12	18	7
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of black marbles = 11 + 18 = 29 

Number of purple marbles = 12 + 7 = 19 

1 u + 3 p = 29 --- (1)

1 u + 1 p = 19 ---(2)

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 29 - 19
3 p - 1 p = 10
2 p = 10

1 p = 10 ÷ 2 = 5

From (2):
1 u + 1 p = 19
1 u + 1 x 5 = 19
1 u + 5 = 19

1 u = 19 - 5 = 14

Number of purple marbles to be removed from Container V to Container U
= 7 - 1 p
= 7 - 1 x 5
= 7 - 5
= 2

Number of black marbles to be removed from Container V to Container U
= 1 u - 11
= 14 - 11
= 3

Total number of purple and black marbles to be removed from Container V to Container U
= 2 + 3
= 5

Answer(s): 5