There were some gold buttons and red buttons. The buttons were packed into 2 bags. At first, Packet B contained 110 buttons and 40% of them were red buttons. Packet C contained 76 buttons and 75% of them were red buttons. How many gold buttons and red buttons in total must be moved from Packet B to Packet C such that 25% of the buttons in Packet B are gold and 50% of the buttons in Packet C are red?

	Packet B		Packet C
Total	110		76
	Red buttons	Gold buttons	Red buttons	Gold buttons
Before	44	66	57	19
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of red buttons in Packet B at first
= 40% x 110
= ⁴⁰₁₀₀ x 110
= 44

Number of gold buttons in Packet B at first
= 110 - 44
= 66

Number of red buttons in Packet C at first
= 75% x 76
= ⁷⁵₁₀₀ x 76
= 57

Number of gold buttons in Packet C at first
= 76 - 57
= 19

Packet B in the end
25% = ²⁵₁₀₀ =¹₄
Red buttons : Gold buttons = 3 : 1

Packet C in the end
50% = ⁵⁰₁₀₀ =¹₂
Red buttons : Gold buttons = 1 : 1

Total number of red buttons = 3 u + 1 p

3 u + 1 p = 44 + 57
3 u + 1 p = 101 

1 p = 101 - 3 u --- (1)

Total number of gold buttons = 1 u + 1 p
1 u + 1 p = 66 + 19
1 u + 1 p = 85

1 p = 85 - 1 u --- (2)

(2) = (1)
85 - 1 u = 101 - 3 u
3 u - 1 u = 101 - 85
2 u = 16

1 u = 16 ÷ 2 = 8

Total number of gold buttons and red buttons that must be moved from Packet B to Packet C
= 110 - 4 u
= 110 - 4 x 8
= 110 - 32
= 78

Answer(s): 78