There were some black marbles and silver marbles. The marbles were packed into 2 bags. At first, Packet U contained 240 marbles and 30% of them were silver marbles. Packet V contained 620 marbles and 60% of them were silver marbles. How many black marbles and silver marbles in total must be moved from Packet U to Packet V such that 25% of the marbles in Packet U are black and 50% of the marbles in Packet V are silver?

	Packet U		Packet V
Total	240		620
	Silver marbles	Black marbles	Silver marbles	Black marbles
Before	72	168	372	248
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of silver marbles in Packet U at first
= 30% x 240
= ³⁰₁₀₀ x 240
= 72

Number of black marbles in Packet U at first
= 240 - 72
= 168

Number of silver marbles in Packet V at first
= 60% x 620
= ⁶⁰₁₀₀ x 620
= 372

Number of black marbles in Packet V at first
= 620 - 372
= 248

Packet U in the end
25% = ²⁵₁₀₀ =¹₄
Silver marbles : Black marbles = 3 : 1

Packet V in the end
50% = ⁵⁰₁₀₀ =¹₂
Silver marbles : Black marbles = 1 : 1

Total number of silver marbles = 3 u + 1 p

3 u + 1 p = 72 + 372
3 u + 1 p = 444 

1 p = 444 - 3 u --- (1)

Total number of black marbles = 1 u + 1 p
1 u + 1 p = 168 + 248
1 u + 1 p = 416

1 p = 416 - 1 u --- (2)

(2) = (1)
416 - 1 u = 444 - 3 u
3 u - 1 u = 444 - 416
2 u = 28

1 u = 28 ÷ 2 = 14

Total number of black marbles and silver marbles that must be moved from Packet U to Packet V
= 240 - 4 u
= 240 - 4 x 14
= 240 - 56
= 184

Answer(s): 184