There were some green buttons and white buttons. The buttons were packed into 2 bags. At first, Packet B contained 250 buttons and 10% of them were white buttons. Packet C contained 1060 buttons and 60% of them were white buttons. How many green buttons and white buttons in total must be moved from Packet B to Packet C such that 25% of the buttons in Packet B are green and 50% of the buttons in Packet C are white?

	Packet B		Packet C
Total	250		1060
	White buttons	Green buttons	White buttons	Green buttons
Before	25	225	636	424
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of white buttons in Packet B at first
= 10% x 250
= ¹⁰₁₀₀ x 250
= 25

Number of green buttons in Packet B at first
= 250 - 25
= 225

Number of white buttons in Packet C at first
= 60% x 1060
= ⁶⁰₁₀₀ x 1060
= 636

Number of green buttons in Packet C at first
= 1060 - 636
= 424

Packet B in the end
25% = ²⁵₁₀₀ =¹₄
White buttons : Green buttons = 3 : 1

Packet C in the end
50% = ⁵⁰₁₀₀ =¹₂
White buttons : Green buttons = 1 : 1

Total number of white buttons = 3 u + 1 p

3 u + 1 p = 25 + 636
3 u + 1 p = 661 

1 p = 661 - 3 u --- (1)

Total number of green buttons = 1 u + 1 p
1 u + 1 p = 225 + 424
1 u + 1 p = 649

1 p = 649 - 1 u --- (2)

(2) = (1)
649 - 1 u = 661 - 3 u
3 u - 1 u = 661 - 649
2 u = 12

1 u = 12 ÷ 2 = 6

Total number of green buttons and white buttons that must be moved from Packet B to Packet C
= 250 - 4 u
= 250 - 4 x 6
= 250 - 24
= 226

Answer(s): 226