There were some purple erasers and gold erasers. The erasers were packed into 2 bags. At first, Packet Y contained 180 erasers and 30% of them were gold erasers. Packet Z contained 450 erasers and 60% of them were gold erasers. How many purple erasers and gold erasers in total must be moved from Packet Y to Packet Z such that 25% of the erasers in Packet Y are purple and 50% of the erasers in Packet Z are gold?

	Packet Y		Packet Z
Total	180		450
	Gold erasers	Purple erasers	Gold erasers	Purple erasers
Before	54	126	270	180
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of gold erasers in Packet Y at first
= 30% x 180
= ³⁰₁₀₀ x 180
= 54

Number of purple erasers in Packet Y at first
= 180 - 54
= 126

Number of gold erasers in Packet Z at first
= 60% x 450
= ⁶⁰₁₀₀ x 450
= 270

Number of purple erasers in Packet Z at first
= 450 - 270
= 180

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

Packet Z 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 = 54 + 270
3 u + 1 p = 324 

1 p = 324 - 3 u --- (1)

Total number of purple erasers = 1 u + 1 p
1 u + 1 p = 126 + 180
1 u + 1 p = 306

1 p = 306 - 1 u --- (2)

(2) = (1)
306 - 1 u = 324 - 3 u
3 u - 1 u = 324 - 306
2 u = 18

1 u = 18 ÷ 2 = 9

Total number of purple erasers and gold erasers that must be moved from Packet Y to Packet Z
= 180 - 4 u
= 180 - 4 x 9
= 180 - 36
= 144

Answer(s): 144