Box R contains 2 purple marbles and 4 black marbles. Box S contains 20 purple marbles and 12 black marbles. How many black marbles and purple marbles must be transferred from Box S to put into Box R so that 50% of the marbles in Box A are purple and 80% of the marbles in Box S are purple?

	Box R		Box S
	Purple marbles	Black marbles	Purple marbles	Black marbles
Before	2	4	20	12
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	4 p	1 p

50% = ⁵⁰₁₀₀ = 12

80% = ⁸⁰₁₀₀ = 45

Number of purple marbles = 2 + 20 = 22 

Number of black marbles = 4 + 12 = 16 

1 u + 4 p = 22 --- (1)

1 u + 1 p = 16 ---(2)

(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 22 - 16
4 p - 1 p = 6
3 p = 6

1 p = 6 ÷ 3 = 2

From (2):
1 u + 1 p = 16
1 u + 1 x 2 = 16
1 u + 2 = 16

1 u = 16 - 2 = 14

Number of black marbles to be transferred from Box S to Box R
= 12 - 1 p
= 12 - 1 x 2
= 12 - 2
= 10

Number of purple marbles to be transferred from Box S to Box R
= 1 u - 2
= 14 - 2
= 12

Total number of black and purple marbles to be transferred from Box S to Box R
= 10 + 12
= 22

Answer(s): 22