There were some white buttons and gold buttons. The buttons were packed into 2 bags. At first, Box C contained 260 buttons and 10% of them were gold buttons. Box D contained 1060 buttons and 60% of them were gold buttons. How many white buttons and gold buttons in total must be moved from Box C to Box D such that 25% of the buttons in Box C are white and 50% of the buttons in Box D are gold?

	Box C		Box D
Total	260		1060
	Gold buttons	White buttons	Gold buttons	White buttons
Before	26	234	636	424
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of gold buttons in Box C at first
= 10% x 260
= ¹⁰₁₀₀ x 260
= 26

Number of white buttons in Box C at first
= 260 - 26
= 234

Number of gold buttons in Box D at first
= 60% x 1060
= ⁶⁰₁₀₀ x 1060
= 636

Number of white buttons in Box D at first
= 1060 - 636
= 424

Box C in the end
25% = ²⁵₁₀₀ =¹₄
Gold buttons : White buttons = 3 : 1

Box D in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold buttons : White buttons = 1 : 1

Total number of gold buttons = 3 u + 1 p

3 u + 1 p = 26 + 636
3 u + 1 p = 662 

1 p = 662 - 3 u --- (1)

Total number of white buttons = 1 u + 1 p
1 u + 1 p = 234 + 424
1 u + 1 p = 658

1 p = 658 - 1 u --- (2)

(2) = (1)
658 - 1 u = 662 - 3 u
3 u - 1 u = 662 - 658
2 u = 4

1 u = 4 ÷ 2 = 2

Total number of white buttons and gold buttons that must be moved from Box C to Box D
= 260 - 4 u
= 260 - 4 x 2
= 260 - 8
= 252

Answer(s): 252