There were some silver cards and purple cards. The cards were packed into 2 bags. At first, Bag J contained 270 cards and 30% of them were purple cards. Bag K contained 220 cards and 80% of them were purple cards. How many silver cards and purple cards in total must be moved from Bag J to Bag K such that 20% of the cards in Bag J are silver and 50% of the cards in Bag K are purple?

	Bag J		Bag K
Total	270		220
	Purple cards	Silver cards	Purple cards	Silver cards
Before	81	189	176	44
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of purple cards in Bag J at first
= 30% x 270
= ³⁰₁₀₀ x 270
= 81

Number of silver cards in Bag J at first
= 270 - 81
= 189

Number of purple cards in Bag K at first
= 80% x 220
= ⁸⁰₁₀₀ x 220
= 176

Number of silver cards in Bag K at first
= 220 - 176
= 44

Bag J in the end
20% = ²⁰₁₀₀ =¹₅
Purple cards : Silver cards = 4 : 1

Bag K in the end
50% = ⁵⁰₁₀₀ =¹₂
Purple cards : Silver cards = 1 : 1

Total number of purple cards = 4 u + 1 p

4 u + 1 p = 81 + 176
4 u + 1 p = 257 

1 p = 257 - 4 u --- (1)

Total number of silver cards = 1 u + 1 p
1 u + 1 p = 189 + 44
1 u + 1 p = 233

1 p = 233 - 1 u --- (2)

(2) = (1)
233 - 1 u = 257 - 4 u
4 u - 1 u = 257 - 233
3 u = 24

1 u = 24 ÷ 3 = 8

Total number of silver cards and purple cards that must be moved from Bag J to Bag K
= 270 - 5 u
= 270 - 5 x 8
= 270 - 40
= 230

Answer(s): 230