There were some grey cards and brown cards. The cards were packed into 2 bags. At first, Packet Q contained 80 cards and 40% of them were brown cards. Packet R contained 60 cards and 75% of them were brown cards. How many grey cards and brown cards in total must be moved from Packet Q to Packet R such that 25% of the cards in Packet Q are grey and 50% of the cards in Packet R are brown?

	Packet Q		Packet R
Total	80		60
	Brown cards	Grey cards	Brown cards	Grey cards
Before	32	48	45	15
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of brown cards in Packet Q at first
= 40% x 80
= ⁴⁰₁₀₀ x 80
= 32

Number of grey cards in Packet Q at first
= 80 - 32
= 48

Number of brown cards in Packet R at first
= 75% x 60
= ⁷⁵₁₀₀ x 60
= 45

Number of grey cards in Packet R at first
= 60 - 45
= 15

Packet Q in the end
25% = ²⁵₁₀₀ =¹₄
Brown cards : Grey cards = 3 : 1

Packet R in the end
50% = ⁵⁰₁₀₀ =¹₂
Brown cards : Grey cards = 1 : 1

Total number of brown cards = 3 u + 1 p

3 u + 1 p = 32 + 45
3 u + 1 p = 77 

1 p = 77 - 3 u --- (1)

Total number of grey cards = 1 u + 1 p
1 u + 1 p = 48 + 15
1 u + 1 p = 63

1 p = 63 - 1 u --- (2)

(2) = (1)
63 - 1 u = 77 - 3 u
3 u - 1 u = 77 - 63
2 u = 14

1 u = 14 ÷ 2 = 7

Total number of grey cards and brown cards that must be moved from Packet Q to Packet R
= 80 - 4 u
= 80 - 4 x 7
= 80 - 28
= 52

Answer(s): 52