There were some red buttons and grey buttons. The buttons were packed into 2 bags. At first, Box S contained 260 buttons and 30% of them were grey buttons. Box T contained 264 buttons and 75% of them were grey buttons. How many red buttons and grey buttons in total must be moved from Box S to Box T such that 30% of the buttons in Box S are red and 50% of the buttons in Box T are grey?

	Box S		Box T
Total	260		264
	Grey buttons	Red buttons	Grey buttons	Red buttons
Before	78	182	198	66
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of grey buttons in Box S at first
= 30% x 260
= ³⁰₁₀₀ x 260
= 78

Number of red buttons in Box S at first
= 260 - 78
= 182

Number of grey buttons in Box T at first
= 75% x 264
= ⁷⁵₁₀₀ x 264
= 198

Number of red buttons in Box T at first
= 264 - 198
= 66

Box S in the end
30% = ³⁰₁₀₀ =³₁₀
Grey buttons : Red buttons = 7 : 3

Box T in the end
50% = ⁵⁰₁₀₀ =¹₂
Grey buttons : Red buttons = 1 : 1

Total number of grey buttons = 7 u + 1 p

7 u + 1 p = 78 + 198
7 u + 1 p = 276 

1 p = 276 - 7 u --- (1)

Total number of red buttons = 3 u + 1 p
3 u + 1 p = 182 + 66
3 u + 1 p = 248

1 p = 248 - 3 u --- (2)

(2) = (1)
248 - 3 u = 276 - 7 u
7 u - 3 u = 276 - 248
4 u = 28

1 u = 28 ÷ 4 = 7

Total number of red buttons and grey buttons that must be moved from Box S to Box T
= 260 - 10 u
= 260 - 10 x 7
= 260 - 70
= 190

Answer(s): 190