There were some blue buttons and white buttons. The buttons were packed into 2 bags. At first, Packet Q contained 200 buttons and 30% of them were white buttons. Packet R contained 160 buttons and 80% of them were white buttons. How many blue buttons and white buttons in total must be moved from Packet Q to Packet R such that 25% of the buttons in Packet Q are blue and 50% of the buttons in Packet R are white?

	Packet Q		Packet R
Total	200		160
	White buttons	Blue buttons	White buttons	Blue buttons
Before	60	140	128	32
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of white buttons in Packet Q at first
= 30% x 200
= ³⁰₁₀₀ x 200
= 60

Number of blue buttons in Packet Q at first
= 200 - 60
= 140

Number of white buttons in Packet R at first
= 80% x 160
= ⁸⁰₁₀₀ x 160
= 128

Number of blue buttons in Packet R at first
= 160 - 128
= 32

Packet Q in the end
25% = ²⁵₁₀₀ =¹₄
White buttons : Blue buttons = 3 : 1

Packet R in the end
50% = ⁵⁰₁₀₀ =¹₂
White buttons : Blue buttons = 1 : 1

Total number of white buttons = 3 u + 1 p

3 u + 1 p = 60 + 128
3 u + 1 p = 188 

1 p = 188 - 3 u --- (1)

Total number of blue buttons = 1 u + 1 p
1 u + 1 p = 140 + 32
1 u + 1 p = 172

1 p = 172 - 1 u --- (2)

(2) = (1)
172 - 1 u = 188 - 3 u
3 u - 1 u = 188 - 172
2 u = 16

1 u = 16 ÷ 2 = 8

Total number of blue buttons and white buttons that must be moved from Packet Q to Packet R
= 200 - 4 u
= 200 - 4 x 8
= 200 - 32
= 168

Answer(s): 168