There were some brown beads and grey beads. The beads were packed into 2 bags. At first, Box U contained 190 beads and 30% of them were grey beads. Box V contained 560 beads and 60% of them were grey beads. How many brown beads and grey beads in total must be moved from Box U to Box V such that 20% of the beads in Box U are brown and 50% of the beads in Box V are grey?

	Box U		Box V
Total	190		560
	Grey beads	Brown beads	Grey beads	Brown beads
Before	57	133	336	224
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of grey beads in Box U at first
= 30% x 190
= ³⁰₁₀₀ x 190
= 57

Number of brown beads in Box U at first
= 190 - 57
= 133

Number of grey beads in Box V at first
= 60% x 560
= ⁶⁰₁₀₀ x 560
= 336

Number of brown beads in Box V at first
= 560 - 336
= 224

Box U in the end
20% = ²⁰₁₀₀ =¹₅
Grey beads : Brown beads = 4 : 1

Box V in the end
50% = ⁵⁰₁₀₀ =¹₂
Grey beads : Brown beads = 1 : 1

Total number of grey beads = 4 u + 1 p

4 u + 1 p = 57 + 336
4 u + 1 p = 393 

1 p = 393 - 4 u --- (1)

Total number of brown beads = 1 u + 1 p
1 u + 1 p = 133 + 224
1 u + 1 p = 357

1 p = 357 - 1 u --- (2)

(2) = (1)
357 - 1 u = 393 - 4 u
4 u - 1 u = 393 - 357
3 u = 36

1 u = 36 ÷ 3 = 12

Total number of brown beads and grey beads that must be moved from Box U to Box V
= 190 - 5 u
= 190 - 5 x 12
= 190 - 60
= 130

Answer(s): 130