There were some red buttons and gold buttons. The buttons were packed into 2 bags. At first, Box F contained 145 buttons and 40% of them were gold buttons. Box G contained 185 buttons and 60% of them were gold buttons. How many red buttons and gold buttons in total must be moved from Box F to Box G such that 30% of the buttons in Box F are red and 50% of the buttons in Box G are gold?

	Box F		Box G
Total	145		185
	Gold buttons	Red buttons	Gold buttons	Red buttons
Before	58	87	111	74
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of gold buttons in Box F at first
= 40% x 145
= ⁴⁰₁₀₀ x 145
= 58

Number of red buttons in Box F at first
= 145 - 58
= 87

Number of gold buttons in Box G at first
= 60% x 185
= ⁶⁰₁₀₀ x 185
= 111

Number of red buttons in Box G at first
= 185 - 111
= 74

Box F in the end
30% = ³⁰₁₀₀ =³₁₀
Gold buttons : Red buttons = 7 : 3

Box G in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold buttons : Red buttons = 1 : 1

Total number of gold buttons = 7 u + 1 p

7 u + 1 p = 58 + 111
7 u + 1 p = 169 

1 p = 169 - 7 u --- (1)

Total number of red buttons = 3 u + 1 p
3 u + 1 p = 87 + 74
3 u + 1 p = 161

1 p = 161 - 3 u --- (2)

(2) = (1)
161 - 3 u = 169 - 7 u
7 u - 3 u = 169 - 161
4 u = 8

1 u = 8 ÷ 4 = 2

Total number of red buttons and gold buttons that must be moved from Box F to Box G
= 145 - 10 u
= 145 - 10 x 2
= 145 - 20
= 125

Answer(s): 125