There were some red stamps and black stamps. The stamps were packed into 2 bags. At first, Box E contained 240 stamps and 10% of them were black stamps. Box F contained 340 stamps and 80% of them were black stamps. How many red stamps and black stamps in total must be moved from Box E to Box F such that 20% of the stamps in Box E are red and 50% of the stamps in Box F are black?

	Box E		Box F
Total	240		340
	Black stamps	Red stamps	Black stamps	Red stamps
Before	24	216	272	68
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of black stamps in Box E at first
= 10% x 240
= ¹⁰₁₀₀ x 240
= 24

Number of red stamps in Box E at first
= 240 - 24
= 216

Number of black stamps in Box F at first
= 80% x 340
= ⁸⁰₁₀₀ x 340
= 272

Number of red stamps in Box F at first
= 340 - 272
= 68

Box E in the end
20% = ²⁰₁₀₀ =¹₅
Black stamps : Red stamps = 4 : 1

Box F in the end
50% = ⁵⁰₁₀₀ =¹₂
Black stamps : Red stamps = 1 : 1

Total number of black stamps = 4 u + 1 p

4 u + 1 p = 24 + 272
4 u + 1 p = 296 

1 p = 296 - 4 u --- (1)

Total number of red stamps = 1 u + 1 p
1 u + 1 p = 216 + 68
1 u + 1 p = 284

1 p = 284 - 1 u --- (2)

(2) = (1)
284 - 1 u = 296 - 4 u
4 u - 1 u = 296 - 284
3 u = 12

1 u = 12 ÷ 3 = 4

Total number of red stamps and black stamps that must be moved from Box E to Box F
= 240 - 5 u
= 240 - 5 x 4
= 240 - 20
= 220

Answer(s): 220