Box P contains 7 silver marbles and 6 purple marbles. Box Q contains 57 silver marbles and 22 purple marbles. How many purple marbles and silver marbles must be moved from Box Q to put into Box P so that 50% of the marbles in Box A are silver and 75% of the marbles in Box Q are silver?

	Box P		Box Q
	Silver marbles	Purple marbles	Silver marbles	Purple marbles
Before	7	6	57	22
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of silver marbles = 7 + 57 = 64 

Number of purple marbles = 6 + 22 = 28 

1 u + 3 p = 64 --- (1)

1 u + 1 p = 28 ---(2)

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 64 - 28
3 p - 1 p = 36
2 p = 36

1 p = 36 ÷ 2 = 18

From (2):
1 u + 1 p = 28
1 u + 1 x 18 = 28
1 u + 18 = 28

1 u = 28 - 18 = 10

Number of purple marbles to be moved from Box Q to Box P
= 22 - 1 p
= 22 - 1 x 18
= 22 - 18
= 4

Number of silver marbles to be moved from Box Q to Box P
= 1 u - 7
= 10 - 7
= 3

Total number of purple and silver marbles to be moved from Box Q to Box P
= 4 + 3
= 7

Answer(s): 7