There were some blue marbles and yellow marbles. The marbles were packed into 2 bags. At first, Packet U contained 240 marbles and 30% of them were yellow marbles. Packet V contained 230 marbles and 80% of them were yellow marbles. How many blue marbles and yellow marbles in total must be moved from Packet U to Packet V such that 20% of the marbles in Packet U are blue and 50% of the marbles in Packet V are yellow?

	Packet U		Packet V
Total	240		230
	Yellow marbles	Blue marbles	Yellow marbles	Blue marbles
Before	72	168	184	46
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

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

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

Number of yellow marbles in Packet V at first
= 80% x 230
= ⁸⁰₁₀₀ x 230
= 184

Number of blue marbles in Packet V at first
= 230 - 184
= 46

Packet U in the end
20% = ²⁰₁₀₀ =¹₅
Yellow marbles : Blue marbles = 4 : 1

Packet V in the end
50% = ⁵⁰₁₀₀ =¹₂
Yellow marbles : Blue marbles = 1 : 1

Total number of yellow marbles = 4 u + 1 p

4 u + 1 p = 72 + 184
4 u + 1 p = 256 

1 p = 256 - 4 u --- (1)

Total number of blue marbles = 1 u + 1 p
1 u + 1 p = 168 + 46
1 u + 1 p = 214

1 p = 214 - 1 u --- (2)

(2) = (1)
214 - 1 u = 256 - 4 u
4 u - 1 u = 256 - 214
3 u = 42

1 u = 42 ÷ 3 = 14

Total number of blue marbles and yellow marbles that must be moved from Packet U to Packet V
= 240 - 5 u
= 240 - 5 x 14
= 240 - 70
= 170

Answer(s): 170