There were some white erasers and black erasers. The erasers were packed into 2 bags. At first, Bag H contained 230 erasers and 30% of them were black erasers. Bag J contained 550 erasers and 60% of them were black erasers. How many white erasers and black erasers in total must be moved from Bag H to Bag J such that 25% of the erasers in Bag H are white and 50% of the erasers in Bag J are black?

	Bag H		Bag J
Total	230		550
	Black erasers	White erasers	Black erasers	White erasers
Before	69	161	330	220
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of black erasers in Bag H at first
= 30% x 230
= ³⁰₁₀₀ x 230
= 69

Number of white erasers in Bag H at first
= 230 - 69
= 161

Number of black erasers in Bag J at first
= 60% x 550
= ⁶⁰₁₀₀ x 550
= 330

Number of white erasers in Bag J at first
= 550 - 330
= 220

Bag H in the end
25% = ²⁵₁₀₀ =¹₄
Black erasers : White erasers = 3 : 1

Bag J in the end
50% = ⁵⁰₁₀₀ =¹₂
Black erasers : White erasers = 1 : 1

Total number of black erasers = 3 u + 1 p

3 u + 1 p = 69 + 330
3 u + 1 p = 399 

1 p = 399 - 3 u --- (1)

Total number of white erasers = 1 u + 1 p
1 u + 1 p = 161 + 220
1 u + 1 p = 381

1 p = 381 - 1 u --- (2)

(2) = (1)
381 - 1 u = 399 - 3 u
3 u - 1 u = 399 - 381
2 u = 18

1 u = 18 ÷ 2 = 9

Total number of white erasers and black erasers that must be moved from Bag H to Bag J
= 230 - 4 u
= 230 - 4 x 9
= 230 - 36
= 194

Answer(s): 194