There were some purple erasers and gold erasers. The erasers were packed into 2 bags. At first, Packet M contained 110 erasers and 40% of them were gold erasers. Packet N contained 70 erasers and 80% of them were gold erasers. How many purple erasers and gold erasers in total must be moved from Packet M to Packet N such that 25% of the erasers in Packet M are purple and 50% of the erasers in Packet N are gold?

	Packet M		Packet N
Total	110		70
	Gold erasers	Purple erasers	Gold erasers	Purple erasers
Before	44	66	56	14
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of gold erasers in Packet M at first
= 40% x 110
= ⁴⁰₁₀₀ x 110
= 44

Number of purple erasers in Packet M at first
= 110 - 44
= 66

Number of gold erasers in Packet N at first
= 80% x 70
= ⁸⁰₁₀₀ x 70
= 56

Number of purple erasers in Packet N at first
= 70 - 56
= 14

Packet M in the end
25% = ²⁵₁₀₀ =¹₄
Gold erasers : Purple erasers = 3 : 1

Packet N in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold erasers : Purple erasers = 1 : 1

Total number of gold erasers = 3 u + 1 p

3 u + 1 p = 44 + 56
3 u + 1 p = 100 

1 p = 100 - 3 u --- (1)

Total number of purple erasers = 1 u + 1 p
1 u + 1 p = 66 + 14
1 u + 1 p = 80

1 p = 80 - 1 u --- (2)

(2) = (1)
80 - 1 u = 100 - 3 u
3 u - 1 u = 100 - 80
2 u = 20

1 u = 20 ÷ 2 = 10

Total number of purple erasers and gold erasers that must be moved from Packet M to Packet N
= 110 - 4 u
= 110 - 4 x 10
= 110 - 40
= 70

Answer(s): 70