There were some gold buttons and blue buttons. The buttons were packed into 2 bags. At first, Bag F contained 80 buttons and 40% of them were blue buttons. Bag G contained 56 buttons and 75% of them were blue buttons. How many gold buttons and blue buttons in total must be moved from Bag F to Bag G such that 25% of the buttons in Bag F are gold and 50% of the buttons in Bag G are blue?

	Bag F		Bag G
Total	80		56
	Blue buttons	Gold buttons	Blue buttons	Gold buttons
Before	32	48	42	14
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of blue buttons in Bag F at first
= 40% x 80
= ⁴⁰₁₀₀ x 80
= 32

Number of gold buttons in Bag F at first
= 80 - 32
= 48

Number of blue buttons in Bag G at first
= 75% x 56
= ⁷⁵₁₀₀ x 56
= 42

Number of gold buttons in Bag G at first
= 56 - 42
= 14

Bag F in the end
25% = ²⁵₁₀₀ =¹₄
Blue buttons : Gold buttons = 3 : 1

Bag G in the end
50% = ⁵⁰₁₀₀ =¹₂
Blue buttons : Gold buttons = 1 : 1

Total number of blue buttons = 3 u + 1 p

3 u + 1 p = 32 + 42
3 u + 1 p = 74 

1 p = 74 - 3 u --- (1)

Total number of gold buttons = 1 u + 1 p
1 u + 1 p = 48 + 14
1 u + 1 p = 62

1 p = 62 - 1 u --- (2)

(2) = (1)
62 - 1 u = 74 - 3 u
3 u - 1 u = 74 - 62
2 u = 12

1 u = 12 ÷ 2 = 6

Total number of gold buttons and blue buttons that must be moved from Bag F to Bag G
= 80 - 4 u
= 80 - 4 x 6
= 80 - 24
= 56

Answer(s): 56