There were some grey erasers and purple erasers. The erasers were packed into 2 bags. At first, Packet W contained 230 erasers and 30% of them were purple erasers. Packet X contained 580 erasers and 60% of them were purple erasers. How many grey erasers and purple erasers in total must be moved from Packet W to Packet X such that 20% of the erasers in Packet W are grey and 50% of the erasers in Packet X are purple?

	Packet W		Packet X
Total	230		580
	Purple erasers	Grey erasers	Purple erasers	Grey erasers
Before	69	161	348	232
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of purple erasers in Packet W at first
= 30% x 230
= ³⁰₁₀₀ x 230
= 69

Number of grey erasers in Packet W at first
= 230 - 69
= 161

Number of purple erasers in Packet X at first
= 60% x 580
= ⁶⁰₁₀₀ x 580
= 348

Number of grey erasers in Packet X at first
= 580 - 348
= 232

Packet W in the end
20% = ²⁰₁₀₀ =¹₅
Purple erasers : Grey erasers = 4 : 1

Packet X in the end
50% = ⁵⁰₁₀₀ =¹₂
Purple erasers : Grey erasers = 1 : 1

Total number of purple erasers = 4 u + 1 p

4 u + 1 p = 69 + 348
4 u + 1 p = 417 

1 p = 417 - 4 u --- (1)

Total number of grey erasers = 1 u + 1 p
1 u + 1 p = 161 + 232
1 u + 1 p = 393

1 p = 393 - 1 u --- (2)

(2) = (1)
393 - 1 u = 417 - 4 u
4 u - 1 u = 417 - 393
3 u = 24

1 u = 24 ÷ 3 = 8

Total number of grey erasers and purple erasers that must be moved from Packet W to Packet X
= 230 - 5 u
= 230 - 5 x 8
= 230 - 40
= 190

Answer(s): 190