There were some brown erasers and grey erasers. The erasers were packed into 2 bags. At first, Box W contained 220 erasers and 30% of them were grey erasers. Box X contained 635 erasers and 60% of them were grey erasers. How many brown erasers and grey erasers in total must be moved from Box W to Box X such that 20% of the erasers in Box W are brown and 50% of the erasers in Box X are grey?

	Box W		Box X
Total	220		635
	Grey erasers	Brown erasers	Grey erasers	Brown erasers
Before	66	154	381	254
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of grey erasers in Box W at first
= 30% x 220
= ³⁰₁₀₀ x 220
= 66

Number of brown erasers in Box W at first
= 220 - 66
= 154

Number of grey erasers in Box X at first
= 60% x 635
= ⁶⁰₁₀₀ x 635
= 381

Number of brown erasers in Box X at first
= 635 - 381
= 254

Box W in the end
20% = ²⁰₁₀₀ =¹₅
Grey erasers : Brown erasers = 4 : 1

Box X in the end
50% = ⁵⁰₁₀₀ =¹₂
Grey erasers : Brown erasers = 1 : 1

Total number of grey erasers = 4 u + 1 p

4 u + 1 p = 66 + 381
4 u + 1 p = 447 

1 p = 447 - 4 u --- (1)

Total number of brown erasers = 1 u + 1 p
1 u + 1 p = 154 + 254
1 u + 1 p = 408

1 p = 408 - 1 u --- (2)

(2) = (1)
408 - 1 u = 447 - 4 u
4 u - 1 u = 447 - 408
3 u = 39

1 u = 39 ÷ 3 = 13

Total number of brown erasers and grey erasers that must be moved from Box W to Box X
= 220 - 5 u
= 220 - 5 x 13
= 220 - 65
= 155

Answer(s): 155