There were some blue beads and purple beads. The beads were packed into 2 bags. At first, Bag C contained 290 beads and 30% of them were purple beads. Bag D contained 660 beads and 60% of them were purple beads. How many blue beads and purple beads in total must be moved from Bag C to Bag D such that 25% of the beads in Bag C are blue and 50% of the beads in Bag D are purple?

	Bag C		Bag D
Total	290		660
	Purple beads	Blue beads	Purple beads	Blue beads
Before	87	203	396	264
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of purple beads in Bag C at first
= 30% x 290
= ³⁰₁₀₀ x 290
= 87

Number of blue beads in Bag C at first
= 290 - 87
= 203

Number of purple beads in Bag D at first
= 60% x 660
= ⁶⁰₁₀₀ x 660
= 396

Number of blue beads in Bag D at first
= 660 - 396
= 264

Bag C in the end
25% = ²⁵₁₀₀ =¹₄
Purple beads : Blue beads = 3 : 1

Bag D in the end
50% = ⁵⁰₁₀₀ =¹₂
Purple beads : Blue beads = 1 : 1

Total number of purple beads = 3 u + 1 p

3 u + 1 p = 87 + 396
3 u + 1 p = 483 

1 p = 483 - 3 u --- (1)

Total number of blue beads = 1 u + 1 p
1 u + 1 p = 203 + 264
1 u + 1 p = 467

1 p = 467 - 1 u --- (2)

(2) = (1)
467 - 1 u = 483 - 3 u
3 u - 1 u = 483 - 467
2 u = 16

1 u = 16 ÷ 2 = 8

Total number of blue beads and purple beads that must be moved from Bag C to Bag D
= 290 - 4 u
= 290 - 4 x 8
= 290 - 32
= 258

Answer(s): 258