There were some purple cards and grey cards. The cards were packed into 2 bags. At first, Packet B contained 160 cards and 30% of them were grey cards. Packet C contained 120 cards and 80% of them were grey cards. How many purple cards and grey cards in total must be moved from Packet B to Packet C such that 30% of the cards in Packet B are purple and 50% of the cards in Packet C are grey?

	Packet B		Packet C
Total	160		120
	Grey cards	Purple cards	Grey cards	Purple cards
Before	48	112	96	24
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of grey cards in Packet B at first
= 30% x 160
= ³⁰₁₀₀ x 160
= 48

Number of purple cards in Packet B at first
= 160 - 48
= 112

Number of grey cards in Packet C at first
= 80% x 120
= ⁸⁰₁₀₀ x 120
= 96

Number of purple cards in Packet C at first
= 120 - 96
= 24

Packet B in the end
30% = ³⁰₁₀₀ =³₁₀
Grey cards : Purple cards = 7 : 3

Packet C in the end
50% = ⁵⁰₁₀₀ =¹₂
Grey cards : Purple cards = 1 : 1

Total number of grey cards = 7 u + 1 p

7 u + 1 p = 48 + 96
7 u + 1 p = 144 

1 p = 144 - 7 u --- (1)

Total number of purple cards = 3 u + 1 p
3 u + 1 p = 112 + 24
3 u + 1 p = 136

1 p = 136 - 3 u --- (2)

(2) = (1)
136 - 3 u = 144 - 7 u
7 u - 3 u = 144 - 136
4 u = 8

1 u = 8 ÷ 4 = 2

Total number of purple cards and grey cards that must be moved from Packet B to Packet C
= 160 - 10 u
= 160 - 10 x 2
= 160 - 20
= 140

Answer(s): 140