There were some green beads and gold beads. The beads were packed into 2 bags. At first, Box L contained 230 beads and 10% of them were gold beads. Box M contained 320 beads and 80% of them were gold beads. How many green beads and gold beads in total must be moved from Box L to Box M such that 25% of the beads in Box L are green and 50% of the beads in Box M are gold?

	Box L		Box M
Total	230		320
	Gold beads	Green beads	Gold beads	Green beads
Before	23	207	256	64
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of gold beads in Box L at first
= 10% x 230
= ¹⁰₁₀₀ x 230
= 23

Number of green beads in Box L at first
= 230 - 23
= 207

Number of gold beads in Box M at first
= 80% x 320
= ⁸⁰₁₀₀ x 320
= 256

Number of green beads in Box M at first
= 320 - 256
= 64

Box L in the end
25% = ²⁵₁₀₀ =¹₄
Gold beads : Green beads = 3 : 1

Box M in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold beads : Green beads = 1 : 1

Total number of gold beads = 3 u + 1 p

3 u + 1 p = 23 + 256
3 u + 1 p = 279 

1 p = 279 - 3 u --- (1)

Total number of green beads = 1 u + 1 p
1 u + 1 p = 207 + 64
1 u + 1 p = 271

1 p = 271 - 1 u --- (2)

(2) = (1)
271 - 1 u = 279 - 3 u
3 u - 1 u = 279 - 271
2 u = 8

1 u = 8 ÷ 2 = 4

Total number of green beads and gold beads that must be moved from Box L to Box M
= 230 - 4 u
= 230 - 4 x 4
= 230 - 16
= 214

Answer(s): 214