There were some green beads and brown beads. The beads were packed into 2 bags. At first, Box F contained 260 beads and 10% of them were brown beads. Box G contained 1115 beads and 60% of them were brown beads. How many green beads and brown beads in total must be moved from Box F to Box G such that 20% of the beads in Box F are green and 50% of the beads in Box G are brown?

	Box F		Box G
Total	260		1115
	Brown beads	Green beads	Brown beads	Green beads
Before	26	234	669	446
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of brown beads in Box F at first
= 10% x 260
= ¹⁰₁₀₀ x 260
= 26

Number of green beads in Box F at first
= 260 - 26
= 234

Number of brown beads in Box G at first
= 60% x 1115
= ⁶⁰₁₀₀ x 1115
= 669

Number of green beads in Box G at first
= 1115 - 669
= 446

Box F in the end
20% = ²⁰₁₀₀ =¹₅
Brown beads : Green beads = 4 : 1

Box G in the end
50% = ⁵⁰₁₀₀ =¹₂
Brown beads : Green beads = 1 : 1

Total number of brown beads = 4 u + 1 p

4 u + 1 p = 26 + 669
4 u + 1 p = 695 

1 p = 695 - 4 u --- (1)

Total number of green beads = 1 u + 1 p
1 u + 1 p = 234 + 446
1 u + 1 p = 680

1 p = 680 - 1 u --- (2)

(2) = (1)
680 - 1 u = 695 - 4 u
4 u - 1 u = 695 - 680
3 u = 15

1 u = 15 ÷ 3 = 5

Total number of green beads and brown beads that must be moved from Box F to Box G
= 260 - 5 u
= 260 - 5 x 5
= 260 - 25
= 235

Answer(s): 235