There were some purple marbles and blue marbles. The marbles were packed into 2 bags. At first, Packet P contained 260 marbles and 10% of them were blue marbles. Packet Q contained 440 marbles and 75% of them were blue marbles. How many purple marbles and blue marbles in total must be moved from Packet P to Packet Q such that 25% of the marbles in Packet P are purple and 50% of the marbles in Packet Q are blue?

	Packet P		Packet Q
Total	260		440
	Blue marbles	Purple marbles	Blue marbles	Purple marbles
Before	26	234	330	110
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of blue marbles in Packet P at first
= 10% x 260
= ¹⁰₁₀₀ x 260
= 26

Number of purple marbles in Packet P at first
= 260 - 26
= 234

Number of blue marbles in Packet Q at first
= 75% x 440
= ⁷⁵₁₀₀ x 440
= 330

Number of purple marbles in Packet Q at first
= 440 - 330
= 110

Packet P in the end
25% = ²⁵₁₀₀ =¹₄
Blue marbles : Purple marbles = 3 : 1

Packet Q in the end
50% = ⁵⁰₁₀₀ =¹₂
Blue marbles : Purple marbles = 1 : 1

Total number of blue marbles = 3 u + 1 p

3 u + 1 p = 26 + 330
3 u + 1 p = 356 

1 p = 356 - 3 u --- (1)

Total number of purple marbles = 1 u + 1 p
1 u + 1 p = 234 + 110
1 u + 1 p = 344

1 p = 344 - 1 u --- (2)

(2) = (1)
344 - 1 u = 356 - 3 u
3 u - 1 u = 356 - 344
2 u = 12

1 u = 12 ÷ 2 = 6

Total number of purple marbles and blue marbles that must be moved from Packet P to Packet Q
= 260 - 4 u
= 260 - 4 x 6
= 260 - 24
= 236

Answer(s): 236