There were some red cards and yellow cards. The cards were packed into 2 bags. At first, Box F contained 200 cards and 30% of them were yellow cards. Box G contained 540 cards and 60% of them were yellow cards. How many red cards and yellow cards in total must be moved from Box F to Box G such that 25% of the cards in Box F are red and 50% of the cards in Box G are yellow?

	Box F		Box G
Total	200		540
	Yellow cards	Red cards	Yellow cards	Red cards
Before	60	140	324	216
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of yellow cards in Box F at first
= 30% x 200
= ³⁰₁₀₀ x 200
= 60

Number of red cards in Box F at first
= 200 - 60
= 140

Number of yellow cards in Box G at first
= 60% x 540
= ⁶⁰₁₀₀ x 540
= 324

Number of red cards in Box G at first
= 540 - 324
= 216

Box F in the end
25% = ²⁵₁₀₀ =¹₄
Yellow cards : Red cards = 3 : 1

Box G in the end
50% = ⁵⁰₁₀₀ =¹₂
Yellow cards : Red cards = 1 : 1

Total number of yellow cards = 3 u + 1 p

3 u + 1 p = 60 + 324
3 u + 1 p = 384 

1 p = 384 - 3 u --- (1)

Total number of red cards = 1 u + 1 p
1 u + 1 p = 140 + 216
1 u + 1 p = 356

1 p = 356 - 1 u --- (2)

(2) = (1)
356 - 1 u = 384 - 3 u
3 u - 1 u = 384 - 356
2 u = 28

1 u = 28 ÷ 2 = 14

Total number of red cards and yellow cards that must be moved from Box F to Box G
= 200 - 4 u
= 200 - 4 x 14
= 200 - 56
= 144

Answer(s): 144