There were some black marbles and silver marbles. The marbles were packed into 2 bags. At first, Packet M contained 180 marbles and 30% of them were silver marbles. Packet N contained 390 marbles and 60% of them were silver marbles. How many black marbles and silver marbles in total must be moved from Packet M to Packet N such that 20% of the marbles in Packet M are black and 50% of the marbles in Packet N are silver?

	Packet M		Packet N
Total	180		390
	Silver marbles	Black marbles	Silver marbles	Black marbles
Before	54	126	234	156
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of silver marbles in Packet M at first
= 30% x 180
= ³⁰₁₀₀ x 180
= 54

Number of black marbles in Packet M at first
= 180 - 54
= 126

Number of silver marbles in Packet N at first
= 60% x 390
= ⁶⁰₁₀₀ x 390
= 234

Number of black marbles in Packet N at first
= 390 - 234
= 156

Packet M in the end
20% = ²⁰₁₀₀ =¹₅
Silver marbles : Black marbles = 4 : 1

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

Total number of silver marbles = 4 u + 1 p

4 u + 1 p = 54 + 234
4 u + 1 p = 288 

1 p = 288 - 4 u --- (1)

Total number of black marbles = 1 u + 1 p
1 u + 1 p = 126 + 156
1 u + 1 p = 282

1 p = 282 - 1 u --- (2)

(2) = (1)
282 - 1 u = 288 - 4 u
4 u - 1 u = 288 - 282
3 u = 6

1 u = 6 ÷ 3 = 2

Total number of black marbles and silver marbles that must be moved from Packet M to Packet N
= 180 - 5 u
= 180 - 5 x 2
= 180 - 10
= 170

Answer(s): 170