There were some purple erasers and silver erasers. The erasers were packed into 2 bags. At first, Packet W contained 280 erasers and 10% of them were silver erasers. Packet X contained 1150 erasers and 60% of them were silver erasers. How many purple erasers and silver erasers in total must be moved from Packet W to Packet X such that 20% of the erasers in Packet W are purple and 50% of the erasers in Packet X are silver?

	Packet W		Packet X
Total	280		1150
	Silver erasers	Purple erasers	Silver erasers	Purple erasers
Before	28	252	690	460
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of silver erasers in Packet W at first
= 10% x 280
= ¹⁰₁₀₀ x 280
= 28

Number of purple erasers in Packet W at first
= 280 - 28
= 252

Number of silver erasers in Packet X at first
= 60% x 1150
= ⁶⁰₁₀₀ x 1150
= 690

Number of purple erasers in Packet X at first
= 1150 - 690
= 460

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

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

Total number of silver erasers = 4 u + 1 p

4 u + 1 p = 28 + 690
4 u + 1 p = 718 

1 p = 718 - 4 u --- (1)

Total number of purple erasers = 1 u + 1 p
1 u + 1 p = 252 + 460
1 u + 1 p = 712

1 p = 712 - 1 u --- (2)

(2) = (1)
712 - 1 u = 718 - 4 u
4 u - 1 u = 718 - 712
3 u = 6

1 u = 6 ÷ 3 = 2

Total number of purple erasers and silver erasers that must be moved from Packet W to Packet X
= 280 - 5 u
= 280 - 5 x 2
= 280 - 10
= 270

Answer(s): 270