There were some pink cards and green cards. The cards were packed into 2 bags. At first, Bag X contained 270 cards and 30% of them were green cards. Bag Y contained 256 cards and 75% of them were green cards. How many pink cards and green cards in total must be moved from Bag X to Bag Y such that 30% of the cards in Bag X are pink and 50% of the cards in Bag Y are green?

	Bag X		Bag Y
Total	270		256
	Green cards	Pink cards	Green cards	Pink cards
Before	81	189	192	64
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of green cards in Bag X at first
= 30% x 270
= ³⁰₁₀₀ x 270
= 81

Number of pink cards in Bag X at first
= 270 - 81
= 189

Number of green cards in Bag Y at first
= 75% x 256
= ⁷⁵₁₀₀ x 256
= 192

Number of pink cards in Bag Y at first
= 256 - 192
= 64

Bag X in the end
30% = ³⁰₁₀₀ =³₁₀
Green cards : Pink cards = 7 : 3

Bag Y in the end
50% = ⁵⁰₁₀₀ =¹₂
Green cards : Pink cards = 1 : 1

Total number of green cards = 7 u + 1 p

7 u + 1 p = 81 + 192
7 u + 1 p = 273 

1 p = 273 - 7 u --- (1)

Total number of pink cards = 3 u + 1 p
3 u + 1 p = 189 + 64
3 u + 1 p = 253

1 p = 253 - 3 u --- (2)

(2) = (1)
253 - 3 u = 273 - 7 u
7 u - 3 u = 273 - 253
4 u = 20

1 u = 20 ÷ 4 = 5

Total number of pink cards and green cards that must be moved from Bag X to Bag Y
= 270 - 10 u
= 270 - 10 x 5
= 270 - 50
= 220

Answer(s): 220