There were some silver buttons and gold buttons. The buttons were packed into 2 bags. At first, Box A contained 80 buttons and 40% of them were gold buttons. Box B contained 160 buttons and 60% of them were gold buttons. How many silver buttons and gold buttons in total must be moved from Box A to Box B such that 30% of the buttons in Box A are silver and 50% of the buttons in Box B are gold?

	Box A		Box B
Total	80		160
	Gold buttons	Silver buttons	Gold buttons	Silver buttons
Before	32	48	96	64
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of gold buttons in Box A at first
= 40% x 80
= ⁴⁰₁₀₀ x 80
= 32

Number of silver buttons in Box A at first
= 80 - 32
= 48

Number of gold buttons in Box B at first
= 60% x 160
= ⁶⁰₁₀₀ x 160
= 96

Number of silver buttons in Box B at first
= 160 - 96
= 64

Box A in the end
30% = ³⁰₁₀₀ =³₁₀
Gold buttons : Silver buttons = 7 : 3

Box B in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold buttons : Silver buttons = 1 : 1

Total number of gold buttons = 7 u + 1 p

7 u + 1 p = 32 + 96
7 u + 1 p = 128 

1 p = 128 - 7 u --- (1)

Total number of silver buttons = 3 u + 1 p
3 u + 1 p = 48 + 64
3 u + 1 p = 112

1 p = 112 - 3 u --- (2)

(2) = (1)
112 - 3 u = 128 - 7 u
7 u - 3 u = 128 - 112
4 u = 16

1 u = 16 ÷ 4 = 4

Total number of silver buttons and gold buttons that must be moved from Box A to Box B
= 80 - 10 u
= 80 - 10 x 4
= 80 - 40
= 40

Answer(s): 40