There were some purple buttons and yellow buttons. The buttons were packed into 2 bags. At first, Box T contained 230 buttons and 30% of them were yellow buttons. Box U contained 520 buttons and 60% of them were yellow buttons. How many purple buttons and yellow buttons in total must be moved from Box T to Box U such that 20% of the buttons in Box T are purple and 50% of the buttons in Box U are yellow?

	Box T		Box U
Total	230		520
	Yellow buttons	Purple buttons	Yellow buttons	Purple buttons
Before	69	161	312	208
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of yellow buttons in Box T at first
= 30% x 230
= ³⁰₁₀₀ x 230
= 69

Number of purple buttons in Box T at first
= 230 - 69
= 161

Number of yellow buttons in Box U at first
= 60% x 520
= ⁶⁰₁₀₀ x 520
= 312

Number of purple buttons in Box U at first
= 520 - 312
= 208

Box T in the end
20% = ²⁰₁₀₀ =¹₅
Yellow buttons : Purple buttons = 4 : 1

Box U in the end
50% = ⁵⁰₁₀₀ =¹₂
Yellow buttons : Purple buttons = 1 : 1

Total number of yellow buttons = 4 u + 1 p

4 u + 1 p = 69 + 312
4 u + 1 p = 381 

1 p = 381 - 4 u --- (1)

Total number of purple buttons = 1 u + 1 p
1 u + 1 p = 161 + 208
1 u + 1 p = 369

1 p = 369 - 1 u --- (2)

(2) = (1)
369 - 1 u = 381 - 4 u
4 u - 1 u = 381 - 369
3 u = 12

1 u = 12 ÷ 3 = 4

Total number of purple buttons and yellow buttons that must be moved from Box T to Box U
= 230 - 5 u
= 230 - 5 x 4
= 230 - 20
= 210

Answer(s): 210