There were some brown cards and blue cards. The cards were packed into 2 bags. At first, Box Q contained 300 cards and 30% of them were blue cards. Box R contained 276 cards and 75% of them were blue cards. How many brown cards and blue cards in total must be moved from Box Q to Box R such that 20% of the cards in Box Q are brown and 50% of the cards in Box R are blue?

	Box Q		Box R
Total	300		276
	Blue cards	Brown cards	Blue cards	Brown cards
Before	90	210	207	69
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of blue cards in Box Q at first
= 30% x 300
= ³⁰₁₀₀ x 300
= 90

Number of brown cards in Box Q at first
= 300 - 90
= 210

Number of blue cards in Box R at first
= 75% x 276
= ⁷⁵₁₀₀ x 276
= 207

Number of brown cards in Box R at first
= 276 - 207
= 69

Box Q in the end
20% = ²⁰₁₀₀ =¹₅
Blue cards : Brown cards = 4 : 1

Box R in the end
50% = ⁵⁰₁₀₀ =¹₂
Blue cards : Brown cards = 1 : 1

Total number of blue cards = 4 u + 1 p

4 u + 1 p = 90 + 207
4 u + 1 p = 297 

1 p = 297 - 4 u --- (1)

Total number of brown cards = 1 u + 1 p
1 u + 1 p = 210 + 69
1 u + 1 p = 279

1 p = 279 - 1 u --- (2)

(2) = (1)
279 - 1 u = 297 - 4 u
4 u - 1 u = 297 - 279
3 u = 18

1 u = 18 ÷ 3 = 6

Total number of brown cards and blue cards that must be moved from Box Q to Box R
= 300 - 5 u
= 300 - 5 x 6
= 300 - 30
= 270

Answer(s): 270