There were some blue buttons and pink buttons. The buttons were packed into 2 bags. At first, Packet U contained 230 buttons and 30% of them were pink buttons. Packet V contained 655 buttons and 60% of them were pink buttons. How many blue buttons and pink buttons in total must be moved from Packet U to Packet V such that 20% of the buttons in Packet U are blue and 50% of the buttons in Packet V are pink?

	Packet U		Packet V
Total	230		655
	Pink buttons	Blue buttons	Pink buttons	Blue buttons
Before	69	161	393	262
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of pink buttons in Packet U at first
= 30% x 230
= ³⁰₁₀₀ x 230
= 69

Number of blue buttons in Packet U at first
= 230 - 69
= 161

Number of pink buttons in Packet V at first
= 60% x 655
= ⁶⁰₁₀₀ x 655
= 393

Number of blue buttons in Packet V at first
= 655 - 393
= 262

Packet U in the end
20% = ²⁰₁₀₀ =¹₅
Pink buttons : Blue buttons = 4 : 1

Packet V in the end
50% = ⁵⁰₁₀₀ =¹₂
Pink buttons : Blue buttons = 1 : 1

Total number of pink buttons = 4 u + 1 p

4 u + 1 p = 69 + 393
4 u + 1 p = 462 

1 p = 462 - 4 u --- (1)

Total number of blue buttons = 1 u + 1 p
1 u + 1 p = 161 + 262
1 u + 1 p = 423

1 p = 423 - 1 u --- (2)

(2) = (1)
423 - 1 u = 462 - 4 u
4 u - 1 u = 462 - 423
3 u = 39

1 u = 39 ÷ 3 = 13

Total number of blue buttons and pink buttons that must be moved from Packet U to Packet V
= 230 - 5 u
= 230 - 5 x 13
= 230 - 65
= 165

Answer(s): 165