There were some blue cards and silver cards. The cards were packed into 2 bags. At first, Packet P contained 200 cards and 30% of them were silver cards. Packet Q contained 180 cards and 80% of them were silver cards. How many blue cards and silver cards in total must be moved from Packet P to Packet Q such that 25% of the cards in Packet P are blue and 50% of the cards in Packet Q are silver?

	Packet P		Packet Q
Total	200		180
	Silver cards	Blue cards	Silver cards	Blue cards
Before	60	140	144	36
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of silver cards in Packet P at first
= 30% x 200
= ³⁰₁₀₀ x 200
= 60

Number of blue cards in Packet P at first
= 200 - 60
= 140

Number of silver cards in Packet Q at first
= 80% x 180
= ⁸⁰₁₀₀ x 180
= 144

Number of blue cards in Packet Q at first
= 180 - 144
= 36

Packet P in the end
25% = ²⁵₁₀₀ =¹₄
Silver cards : Blue cards = 3 : 1

Packet Q in the end
50% = ⁵⁰₁₀₀ =¹₂
Silver cards : Blue cards = 1 : 1

Total number of silver cards = 3 u + 1 p

3 u + 1 p = 60 + 144
3 u + 1 p = 204 

1 p = 204 - 3 u --- (1)

Total number of blue cards = 1 u + 1 p
1 u + 1 p = 140 + 36
1 u + 1 p = 176

1 p = 176 - 1 u --- (2)

(2) = (1)
176 - 1 u = 204 - 3 u
3 u - 1 u = 204 - 176
2 u = 28

1 u = 28 ÷ 2 = 14

Total number of blue cards and silver cards that must be moved from Packet P to Packet Q
= 200 - 4 u
= 200 - 4 x 14
= 200 - 56
= 144

Answer(s): 144