There were some silver marbles and purple marbles. The marbles were packed into 2 bags. At first, Packet S contained 160 marbles and 10% of them were purple marbles. Packet T contained 670 marbles and 60% of them were purple marbles. How many silver marbles and purple marbles in total must be moved from Packet S to Packet T such that 20% of the marbles in Packet S are silver and 50% of the marbles in Packet T are purple?

	Packet S		Packet T
Total	160		670
	Purple marbles	Silver marbles	Purple marbles	Silver marbles
Before	16	144	402	268
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of purple marbles in Packet S at first
= 10% x 160
= ¹⁰₁₀₀ x 160
= 16

Number of silver marbles in Packet S at first
= 160 - 16
= 144

Number of purple marbles in Packet T at first
= 60% x 670
= ⁶⁰₁₀₀ x 670
= 402

Number of silver marbles in Packet T at first
= 670 - 402
= 268

Packet S in the end
20% = ²⁰₁₀₀ =¹₅
Purple marbles : Silver marbles = 4 : 1

Packet T in the end
50% = ⁵⁰₁₀₀ =¹₂
Purple marbles : Silver marbles = 1 : 1

Total number of purple marbles = 4 u + 1 p

4 u + 1 p = 16 + 402
4 u + 1 p = 418 

1 p = 418 - 4 u --- (1)

Total number of silver marbles = 1 u + 1 p
1 u + 1 p = 144 + 268
1 u + 1 p = 412

1 p = 412 - 1 u --- (2)

(2) = (1)
412 - 1 u = 418 - 4 u
4 u - 1 u = 418 - 412
3 u = 6

1 u = 6 ÷ 3 = 2

Total number of silver marbles and purple marbles that must be moved from Packet S to Packet T
= 160 - 5 u
= 160 - 5 x 2
= 160 - 10
= 150

Answer(s): 150