There were some red buttons and silver buttons. The buttons were packed into 2 bags. At first, Box T contained 280 buttons and 30% of them were silver buttons. Box U contained 780 buttons and 60% of them were silver buttons. How many red buttons and silver buttons in total must be moved from Box T to Box U such that 30% of the buttons in Box T are red and 50% of the buttons in Box U are silver?

	Box T		Box U
Total	280		780
	Silver buttons	Red buttons	Silver buttons	Red buttons
Before	84	196	468	312
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of silver buttons in Box T at first
= 30% x 280
= ³⁰₁₀₀ x 280
= 84

Number of red buttons in Box T at first
= 280 - 84
= 196

Number of silver buttons in Box U at first
= 60% x 780
= ⁶⁰₁₀₀ x 780
= 468

Number of red buttons in Box U at first
= 780 - 468
= 312

Box T in the end
30% = ³⁰₁₀₀ =³₁₀
Silver buttons : Red buttons = 7 : 3

Box U in the end
50% = ⁵⁰₁₀₀ =¹₂
Silver buttons : Red buttons = 1 : 1

Total number of silver buttons = 7 u + 1 p

7 u + 1 p = 84 + 468
7 u + 1 p = 552 

1 p = 552 - 7 u --- (1)

Total number of red buttons = 3 u + 1 p
3 u + 1 p = 196 + 312
3 u + 1 p = 508

1 p = 508 - 3 u --- (2)

(2) = (1)
508 - 3 u = 552 - 7 u
7 u - 3 u = 552 - 508
4 u = 44

1 u = 44 ÷ 4 = 11

Total number of red buttons and silver buttons that must be moved from Box T to Box U
= 280 - 10 u
= 280 - 10 x 11
= 280 - 110
= 170

Answer(s): 170