There were some grey cards and green cards. The cards were packed into 2 bags. At first, Box X contained 300 cards and 30% of them were green cards. Box Y contained 690 cards and 60% of them were green cards. How many grey cards and green cards in total must be moved from Box X to Box Y such that 20% of the cards in Box X are grey and 50% of the cards in Box Y are green?

	Box X		Box Y
Total	300		690
	Green cards	Grey cards	Green cards	Grey cards
Before	90	210	414	276
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of green cards in Box X at first
= 30% x 300
= ³⁰₁₀₀ x 300
= 90

Number of grey cards in Box X at first
= 300 - 90
= 210

Number of green cards in Box Y at first
= 60% x 690
= ⁶⁰₁₀₀ x 690
= 414

Number of grey cards in Box Y at first
= 690 - 414
= 276

Box X in the end
20% = ²⁰₁₀₀ =¹₅
Green cards : Grey cards = 4 : 1

Box Y in the end
50% = ⁵⁰₁₀₀ =¹₂
Green cards : Grey cards = 1 : 1

Total number of green cards = 4 u + 1 p

4 u + 1 p = 90 + 414
4 u + 1 p = 504 

1 p = 504 - 4 u --- (1)

Total number of grey cards = 1 u + 1 p
1 u + 1 p = 210 + 276
1 u + 1 p = 486

1 p = 486 - 1 u --- (2)

(2) = (1)
486 - 1 u = 504 - 4 u
4 u - 1 u = 504 - 486
3 u = 18

1 u = 18 ÷ 3 = 6

Total number of grey cards and green cards that must be moved from Box X to Box Y
= 300 - 5 u
= 300 - 5 x 6
= 300 - 30
= 270

Answer(s): 270