There were some pink beads and black beads. The beads were packed into 2 bags. At first, Packet F contained 140 beads and 40% of them were black beads. Packet G contained 80 beads and 75% of them were black beads. How many pink beads and black beads in total must be moved from Packet F to Packet G such that 20% of the beads in Packet F are pink and 50% of the beads in Packet G are black?

	Packet F		Packet G
Total	140		80
	Black beads	Pink beads	Black beads	Pink beads
Before	56	84	60	20
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of black beads in Packet F at first
= 40% x 140
= ⁴⁰₁₀₀ x 140
= 56

Number of pink beads in Packet F at first
= 140 - 56
= 84

Number of black beads in Packet G at first
= 75% x 80
= ⁷⁵₁₀₀ x 80
= 60

Number of pink beads in Packet G at first
= 80 - 60
= 20

Packet F in the end
20% = ²⁰₁₀₀ =¹₅
Black beads : Pink beads = 4 : 1

Packet G in the end
50% = ⁵⁰₁₀₀ =¹₂
Black beads : Pink beads = 1 : 1

Total number of black beads = 4 u + 1 p

4 u + 1 p = 56 + 60
4 u + 1 p = 116 

1 p = 116 - 4 u --- (1)

Total number of pink beads = 1 u + 1 p
1 u + 1 p = 84 + 20
1 u + 1 p = 104

1 p = 104 - 1 u --- (2)

(2) = (1)
104 - 1 u = 116 - 4 u
4 u - 1 u = 116 - 104
3 u = 12

1 u = 12 ÷ 3 = 4

Total number of pink beads and black beads that must be moved from Packet F to Packet G
= 140 - 5 u
= 140 - 5 x 4
= 140 - 20
= 120

Answer(s): 120