There were some black beads and blue beads. The beads were packed into 2 bags. At first, Bag N contained 240 beads and 30% of them were blue beads. Bag P contained 200 beads and 80% of them were blue beads. How many black beads and blue beads in total must be moved from Bag N to Bag P such that 20% of the beads in Bag N are black and 50% of the beads in Bag P are blue?

	Bag N		Bag P
Total	240		200
	Blue beads	Black beads	Blue beads	Black beads
Before	72	168	160	40
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of blue beads in Bag N at first
= 30% x 240
= ³⁰₁₀₀ x 240
= 72

Number of black beads in Bag N at first
= 240 - 72
= 168

Number of blue beads in Bag P at first
= 80% x 200
= ⁸⁰₁₀₀ x 200
= 160

Number of black beads in Bag P at first
= 200 - 160
= 40

Bag N in the end
20% = ²⁰₁₀₀ =¹₅
Blue beads : Black beads = 4 : 1

Bag P in the end
50% = ⁵⁰₁₀₀ =¹₂
Blue beads : Black beads = 1 : 1

Total number of blue beads = 4 u + 1 p

4 u + 1 p = 72 + 160
4 u + 1 p = 232 

1 p = 232 - 4 u --- (1)

Total number of black beads = 1 u + 1 p
1 u + 1 p = 168 + 40
1 u + 1 p = 208

1 p = 208 - 1 u --- (2)

(2) = (1)
208 - 1 u = 232 - 4 u
4 u - 1 u = 232 - 208
3 u = 24

1 u = 24 ÷ 3 = 8

Total number of black beads and blue beads that must be moved from Bag N to Bag P
= 240 - 5 u
= 240 - 5 x 8
= 240 - 40
= 200

Answer(s): 200