There were some brown beads and gold beads. The beads were packed into 2 bags. At first, Bag H contained 150 beads and 30% of them were gold beads. Bag J contained 430 beads and 60% of them were gold beads. How many brown beads and gold beads in total must be moved from Bag H to Bag J such that 25% of the beads in Bag H are brown and 50% of the beads in Bag J are gold?

	Bag H		Bag J
Total	150		430
	Gold beads	Brown beads	Gold beads	Brown beads
Before	45	105	258	172
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of gold beads in Bag H at first
= 30% x 150
= ³⁰₁₀₀ x 150
= 45

Number of brown beads in Bag H at first
= 150 - 45
= 105

Number of gold beads in Bag J at first
= 60% x 430
= ⁶⁰₁₀₀ x 430
= 258

Number of brown beads in Bag J at first
= 430 - 258
= 172

Bag H in the end
25% = ²⁵₁₀₀ =¹₄
Gold beads : Brown beads = 3 : 1

Bag J in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold beads : Brown beads = 1 : 1

Total number of gold beads = 3 u + 1 p

3 u + 1 p = 45 + 258
3 u + 1 p = 303 

1 p = 303 - 3 u --- (1)

Total number of brown beads = 1 u + 1 p
1 u + 1 p = 105 + 172
1 u + 1 p = 277

1 p = 277 - 1 u --- (2)

(2) = (1)
277 - 1 u = 303 - 3 u
3 u - 1 u = 303 - 277
2 u = 26

1 u = 26 ÷ 2 = 13

Total number of brown beads and gold beads that must be moved from Bag H to Bag J
= 150 - 4 u
= 150 - 4 x 13
= 150 - 52
= 98

Answer(s): 98