There were some red beads and yellow beads. The beads were packed into 2 bags. At first, Packet L contained 100 beads and 40% of them were yellow beads. Packet M contained 150 beads and 60% of them were yellow beads. How many red beads and yellow beads in total must be moved from Packet L to Packet M such that 25% of the beads in Packet L are red and 50% of the beads in Packet M are yellow?

	Packet L		Packet M
Total	100		150
	Yellow beads	Red beads	Yellow beads	Red beads
Before	40	60	90	60
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of yellow beads in Packet L at first
= 40% x 100
= ⁴⁰₁₀₀ x 100
= 40

Number of red beads in Packet L at first
= 100 - 40
= 60

Number of yellow beads in Packet M at first
= 60% x 150
= ⁶⁰₁₀₀ x 150
= 90

Number of red beads in Packet M at first
= 150 - 90
= 60

Packet L in the end
25% = ²⁵₁₀₀ =¹₄
Yellow beads : Red beads = 3 : 1

Packet M in the end
50% = ⁵⁰₁₀₀ =¹₂
Yellow beads : Red beads = 1 : 1

Total number of yellow beads = 3 u + 1 p

3 u + 1 p = 40 + 90
3 u + 1 p = 130 

1 p = 130 - 3 u --- (1)

Total number of red beads = 1 u + 1 p
1 u + 1 p = 60 + 60
1 u + 1 p = 120

1 p = 120 - 1 u --- (2)

(2) = (1)
120 - 1 u = 130 - 3 u
3 u - 1 u = 130 - 120
2 u = 10

1 u = 10 ÷ 2 = 5

Total number of red beads and yellow beads that must be moved from Packet L to Packet M
= 100 - 4 u
= 100 - 4 x 5
= 100 - 20
= 80

Answer(s): 80