There were some gold erasers and blue erasers. The erasers were packed into 2 bags. At first, Box B contained 260 erasers and 30% of them were blue erasers. Box C contained 560 erasers and 60% of them were blue erasers. How many gold erasers and blue erasers in total must be moved from Box B to Box C such that 25% of the erasers in Box B are gold and 50% of the erasers in Box C are blue?

	Box B		Box C
Total	260		560
	Blue erasers	Gold erasers	Blue erasers	Gold erasers
Before	78	182	336	224
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of blue erasers in Box B at first
= 30% x 260
= ³⁰₁₀₀ x 260
= 78

Number of gold erasers in Box B at first
= 260 - 78
= 182

Number of blue erasers in Box C at first
= 60% x 560
= ⁶⁰₁₀₀ x 560
= 336

Number of gold erasers in Box C at first
= 560 - 336
= 224

Box B in the end
25% = ²⁵₁₀₀ =¹₄
Blue erasers : Gold erasers = 3 : 1

Box C in the end
50% = ⁵⁰₁₀₀ =¹₂
Blue erasers : Gold erasers = 1 : 1

Total number of blue erasers = 3 u + 1 p

3 u + 1 p = 78 + 336
3 u + 1 p = 414 

1 p = 414 - 3 u --- (1)

Total number of gold erasers = 1 u + 1 p
1 u + 1 p = 182 + 224
1 u + 1 p = 406

1 p = 406 - 1 u --- (2)

(2) = (1)
406 - 1 u = 414 - 3 u
3 u - 1 u = 414 - 406
2 u = 8

1 u = 8 ÷ 2 = 4

Total number of gold erasers and blue erasers that must be moved from Box B to Box C
= 260 - 4 u
= 260 - 4 x 4
= 260 - 16
= 244

Answer(s): 244