There were some silver buttons and red buttons. The buttons were packed into 2 bags. At first, Packet F contained 140 buttons and 40% of them were red buttons. Packet G contained 260 buttons and 60% of them were red buttons. How many silver buttons and red buttons in total must be moved from Packet F to Packet G such that 30% of the buttons in Packet F are silver and 50% of the buttons in Packet G are red?

	Packet F		Packet G
Total	140		260
	Red buttons	Silver buttons	Red buttons	Silver buttons
Before	56	84	156	104
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of red buttons in Packet F at first
= 40% x 140
= ⁴⁰₁₀₀ x 140
= 56

Number of silver buttons in Packet F at first
= 140 - 56
= 84

Number of red buttons in Packet G at first
= 60% x 260
= ⁶⁰₁₀₀ x 260
= 156

Number of silver buttons in Packet G at first
= 260 - 156
= 104

Packet F in the end
30% = ³⁰₁₀₀ =³₁₀
Red buttons : Silver buttons = 7 : 3

Packet G in the end
50% = ⁵⁰₁₀₀ =¹₂
Red buttons : Silver buttons = 1 : 1

Total number of red buttons = 7 u + 1 p

7 u + 1 p = 56 + 156
7 u + 1 p = 212 

1 p = 212 - 7 u --- (1)

Total number of silver buttons = 3 u + 1 p
3 u + 1 p = 84 + 104
3 u + 1 p = 188

1 p = 188 - 3 u --- (2)

(2) = (1)
188 - 3 u = 212 - 7 u
7 u - 3 u = 212 - 188
4 u = 24

1 u = 24 ÷ 4 = 6

Total number of silver buttons and red buttons that must be moved from Packet F to Packet G
= 140 - 10 u
= 140 - 10 x 6
= 140 - 60
= 80

Answer(s): 80