There were some purple stamps and pink stamps. The stamps were packed into 2 bags. At first, Packet X contained 180 stamps and 10% of them were pink stamps. Packet Y contained 780 stamps and 60% of them were pink stamps. How many purple stamps and pink stamps in total must be moved from Packet X to Packet Y such that 20% of the stamps in Packet X are purple and 50% of the stamps in Packet Y are pink?

	Packet X		Packet Y
Total	180		780
	Pink stamps	Purple stamps	Pink stamps	Purple stamps
Before	18	162	468	312
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of pink stamps in Packet X at first
= 10% x 180
= ¹⁰₁₀₀ x 180
= 18

Number of purple stamps in Packet X at first
= 180 - 18
= 162

Number of pink stamps in Packet Y at first
= 60% x 780
= ⁶⁰₁₀₀ x 780
= 468

Number of purple stamps in Packet Y at first
= 780 - 468
= 312

Packet X in the end
20% = ²⁰₁₀₀ =¹₅
Pink stamps : Purple stamps = 4 : 1

Packet Y in the end
50% = ⁵⁰₁₀₀ =¹₂
Pink stamps : Purple stamps = 1 : 1

Total number of pink stamps = 4 u + 1 p

4 u + 1 p = 18 + 468
4 u + 1 p = 486 

1 p = 486 - 4 u --- (1)

Total number of purple stamps = 1 u + 1 p
1 u + 1 p = 162 + 312
1 u + 1 p = 474

1 p = 474 - 1 u --- (2)

(2) = (1)
474 - 1 u = 486 - 4 u
4 u - 1 u = 486 - 474
3 u = 12

1 u = 12 ÷ 3 = 4

Total number of purple stamps and pink stamps that must be moved from Packet X to Packet Y
= 180 - 5 u
= 180 - 5 x 4
= 180 - 20
= 160

Answer(s): 160