There were some red cards and purple cards. The cards were packed into 2 bags. At first, Packet E contained 210 cards and 30% of them were purple cards. Packet F contained 555 cards and 60% of them were purple cards. How many red cards and purple cards in total must be moved from Packet E to Packet F such that 20% of the cards in Packet E are red and 50% of the cards in Packet F are purple?

	Packet E		Packet F
Total	210		555
	Purple cards	Red cards	Purple cards	Red cards
Before	63	147	333	222
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of purple cards in Packet E at first
= 30% x 210
= ³⁰₁₀₀ x 210
= 63

Number of red cards in Packet E at first
= 210 - 63
= 147

Number of purple cards in Packet F at first
= 60% x 555
= ⁶⁰₁₀₀ x 555
= 333

Number of red cards in Packet F at first
= 555 - 333
= 222

Packet E in the end
20% = ²⁰₁₀₀ =¹₅
Purple cards : Red cards = 4 : 1

Packet F in the end
50% = ⁵⁰₁₀₀ =¹₂
Purple cards : Red cards = 1 : 1

Total number of purple cards = 4 u + 1 p

4 u + 1 p = 63 + 333
4 u + 1 p = 396 

1 p = 396 - 4 u --- (1)

Total number of red cards = 1 u + 1 p
1 u + 1 p = 147 + 222
1 u + 1 p = 369

1 p = 369 - 1 u --- (2)

(2) = (1)
369 - 1 u = 396 - 4 u
4 u - 1 u = 396 - 369
3 u = 27

1 u = 27 ÷ 3 = 9

Total number of red cards and purple cards that must be moved from Packet E to Packet F
= 210 - 5 u
= 210 - 5 x 9
= 210 - 45
= 165

Answer(s): 165