There were some purple erasers and yellow erasers. The erasers were packed into 2 bags. At first, Bag W contained 250 erasers and 30% of them were yellow erasers. Bag X contained 680 erasers and 60% of them were yellow erasers. How many purple erasers and yellow erasers in total must be moved from Bag W to Bag X such that 20% of the erasers in Bag W are purple and 50% of the erasers in Bag X are yellow?

	Bag W		Bag X
Total	250		680
	Yellow erasers	Purple erasers	Yellow erasers	Purple erasers
Before	75	175	408	272
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of yellow erasers in Bag W at first
= 30% x 250
= ³⁰₁₀₀ x 250
= 75

Number of purple erasers in Bag W at first
= 250 - 75
= 175

Number of yellow erasers in Bag X at first
= 60% x 680
= ⁶⁰₁₀₀ x 680
= 408

Number of purple erasers in Bag X at first
= 680 - 408
= 272

Bag W in the end
20% = ²⁰₁₀₀ =¹₅
Yellow erasers : Purple erasers = 4 : 1

Bag X in the end
50% = ⁵⁰₁₀₀ =¹₂
Yellow erasers : Purple erasers = 1 : 1

Total number of yellow erasers = 4 u + 1 p

4 u + 1 p = 75 + 408
4 u + 1 p = 483 

1 p = 483 - 4 u --- (1)

Total number of purple erasers = 1 u + 1 p
1 u + 1 p = 175 + 272
1 u + 1 p = 447

1 p = 447 - 1 u --- (2)

(2) = (1)
447 - 1 u = 483 - 4 u
4 u - 1 u = 483 - 447
3 u = 36

1 u = 36 ÷ 3 = 12

Total number of purple erasers and yellow erasers that must be moved from Bag W to Bag X
= 250 - 5 u
= 250 - 5 x 12
= 250 - 60
= 190

Answer(s): 190