Box R contains 6 grey marbles and 12 purple marbles. Box S contains 65 grey marbles and 25 purple marbles. How many purple marbles and grey marbles must be moved from Box S to put into Box R so that 50% of the marbles in Box A are grey and 75% of the marbles in Box S are grey?

	Box R		Box S
	Grey marbles	Purple marbles	Grey marbles	Purple marbles
Before	6	12	65	25
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of grey marbles = 6 + 65 = 71 

Number of purple marbles = 12 + 25 = 37 

1 u + 3 p = 71 --- (1)

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

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 71 - 37
3 p - 1 p = 34
2 p = 34

1 p = 34 ÷ 2 = 17

From (2):
1 u + 1 p = 37
1 u + 1 x 17 = 37
1 u + 17 = 37

1 u = 37 - 17 = 20

Number of purple marbles to be moved from Box S to Box R
= 25 - 1 p
= 25 - 1 x 17
= 25 - 17
= 8

Number of grey marbles to be moved from Box S to Box R
= 1 u - 6
= 20 - 6
= 14

Total number of purple and grey marbles to be moved from Box S to Box R
= 8 + 14
= 22

Answer(s): 22