There were some silver cards and blue cards. The cards were packed into 2 bags. At first, Bag B contained 130 cards and 40% of them were blue cards. Bag C contained 250 cards and 60% of them were blue cards. How many silver cards and blue cards in total must be moved from Bag B to Bag C such that 25% of the cards in Bag B are silver and 50% of the cards in Bag C are blue?

	Bag B		Bag C
Total	130		250
	Blue cards	Silver cards	Blue cards	Silver cards
Before	52	78	150	100
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of blue cards in Bag B at first
= 40% x 130
= ⁴⁰₁₀₀ x 130
= 52

Number of silver cards in Bag B at first
= 130 - 52
= 78

Number of blue cards in Bag C at first
= 60% x 250
= ⁶⁰₁₀₀ x 250
= 150

Number of silver cards in Bag C at first
= 250 - 150
= 100

Bag B in the end
25% = ²⁵₁₀₀ =¹₄
Blue cards : Silver cards = 3 : 1

Bag C in the end
50% = ⁵⁰₁₀₀ =¹₂
Blue cards : Silver cards = 1 : 1

Total number of blue cards = 3 u + 1 p

3 u + 1 p = 52 + 150
3 u + 1 p = 202 

1 p = 202 - 3 u --- (1)

Total number of silver cards = 1 u + 1 p
1 u + 1 p = 78 + 100
1 u + 1 p = 178

1 p = 178 - 1 u --- (2)

(2) = (1)
178 - 1 u = 202 - 3 u
3 u - 1 u = 202 - 178
2 u = 24

1 u = 24 ÷ 2 = 12

Total number of silver cards and blue cards that must be moved from Bag B to Bag C
= 130 - 4 u
= 130 - 4 x 12
= 130 - 48
= 82

Answer(s): 82