There were some white cards and silver cards. The cards were packed into 2 bags. At first, Bag D contained 180 cards and 30% of them were silver cards. Bag E contained 495 cards and 60% of them were silver cards. How many white cards and silver cards in total must be moved from Bag D to Bag E such that 20% of the cards in Bag D are white and 50% of the cards in Bag E are silver?

	Bag D		Bag E
Total	180		495
	Silver cards	White cards	Silver cards	White cards
Before	54	126	297	198
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of silver cards in Bag D at first
= 30% x 180
= ³⁰₁₀₀ x 180
= 54

Number of white cards in Bag D at first
= 180 - 54
= 126

Number of silver cards in Bag E at first
= 60% x 495
= ⁶⁰₁₀₀ x 495
= 297

Number of white cards in Bag E at first
= 495 - 297
= 198

Bag D in the end
20% = ²⁰₁₀₀ =¹₅
Silver cards : White cards = 4 : 1

Bag E in the end
50% = ⁵⁰₁₀₀ =¹₂
Silver cards : White cards = 1 : 1

Total number of silver cards = 4 u + 1 p

4 u + 1 p = 54 + 297
4 u + 1 p = 351 

1 p = 351 - 4 u --- (1)

Total number of white cards = 1 u + 1 p
1 u + 1 p = 126 + 198
1 u + 1 p = 324

1 p = 324 - 1 u --- (2)

(2) = (1)
324 - 1 u = 351 - 4 u
4 u - 1 u = 351 - 324
3 u = 27

1 u = 27 ÷ 3 = 9

Total number of white cards and silver cards that must be moved from Bag D to Bag E
= 180 - 5 u
= 180 - 5 x 9
= 180 - 45
= 135

Answer(s): 135