There were some white stamps and gold stamps. The stamps were packed into 2 bags. At first, Bag P contained 270 stamps and 30% of them were gold stamps. Bag Q contained 205 stamps and 80% of them were gold stamps. How many white stamps and gold stamps in total must be moved from Bag P to Bag Q such that 20% of the stamps in Bag P are white and 50% of the stamps in Bag Q are gold?

	Bag P		Bag Q
Total	270		205
	Gold stamps	White stamps	Gold stamps	White stamps
Before	81	189	164	41
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of gold stamps in Bag P at first
= 30% x 270
= ³⁰₁₀₀ x 270
= 81

Number of white stamps in Bag P at first
= 270 - 81
= 189

Number of gold stamps in Bag Q at first
= 80% x 205
= ⁸⁰₁₀₀ x 205
= 164

Number of white stamps in Bag Q at first
= 205 - 164
= 41

Bag P in the end
20% = ²⁰₁₀₀ =¹₅
Gold stamps : White stamps = 4 : 1

Bag Q in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold stamps : White stamps = 1 : 1

Total number of gold stamps = 4 u + 1 p

4 u + 1 p = 81 + 164
4 u + 1 p = 245 

1 p = 245 - 4 u --- (1)

Total number of white stamps = 1 u + 1 p
1 u + 1 p = 189 + 41
1 u + 1 p = 230

1 p = 230 - 1 u --- (2)

(2) = (1)
230 - 1 u = 245 - 4 u
4 u - 1 u = 245 - 230
3 u = 15

1 u = 15 ÷ 3 = 5

Total number of white stamps and gold stamps that must be moved from Bag P to Bag Q
= 270 - 5 u
= 270 - 5 x 5
= 270 - 25
= 245

Answer(s): 245