There were some red stamps and yellow stamps. The stamps were packed into 2 bags. At first, Box C contained 135 stamps and 40% of them were yellow stamps. Box D contained 55 stamps and 80% of them were yellow stamps. How many red stamps and yellow stamps in total must be moved from Box C to Box D such that 20% of the stamps in Box C are red and 50% of the stamps in Box D are yellow?

	Box C		Box D
Total	135		55
	Yellow stamps	Red stamps	Yellow stamps	Red stamps
Before	54	81	44	11
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of yellow stamps in Box C at first
= 40% x 135
= ⁴⁰₁₀₀ x 135
= 54

Number of red stamps in Box C at first
= 135 - 54
= 81

Number of yellow stamps in Box D at first
= 80% x 55
= ⁸⁰₁₀₀ x 55
= 44

Number of red stamps in Box D at first
= 55 - 44
= 11

Box C in the end
20% = ²⁰₁₀₀ =¹₅
Yellow stamps : Red stamps = 4 : 1

Box D in the end
50% = ⁵⁰₁₀₀ =¹₂
Yellow stamps : Red stamps = 1 : 1

Total number of yellow stamps = 4 u + 1 p

4 u + 1 p = 54 + 44
4 u + 1 p = 98 

1 p = 98 - 4 u --- (1)

Total number of red stamps = 1 u + 1 p
1 u + 1 p = 81 + 11
1 u + 1 p = 92

1 p = 92 - 1 u --- (2)

(2) = (1)
92 - 1 u = 98 - 4 u
4 u - 1 u = 98 - 92
3 u = 6

1 u = 6 ÷ 3 = 2

Total number of red stamps and yellow stamps that must be moved from Box C to Box D
= 135 - 5 u
= 135 - 5 x 2
= 135 - 10
= 125

Answer(s): 125