There were some gold buttons and green buttons. The buttons were packed into 2 bags. At first, Box Q contained 250 buttons and 30% of them were green buttons. Box R contained 660 buttons and 60% of them were green buttons. How many gold buttons and green buttons in total must be moved from Box Q to Box R such that 30% of the buttons in Box Q are gold and 50% of the buttons in Box R are green?

	Box Q		Box R
Total	250		660
	Green buttons	Gold buttons	Green buttons	Gold buttons
Before	75	175	396	264
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of green buttons in Box Q at first
= 30% x 250
= ³⁰₁₀₀ x 250
= 75

Number of gold buttons in Box Q at first
= 250 - 75
= 175

Number of green buttons in Box R at first
= 60% x 660
= ⁶⁰₁₀₀ x 660
= 396

Number of gold buttons in Box R at first
= 660 - 396
= 264

Box Q in the end
30% = ³⁰₁₀₀ =³₁₀
Green buttons : Gold buttons = 7 : 3

Box R in the end
50% = ⁵⁰₁₀₀ =¹₂
Green buttons : Gold buttons = 1 : 1

Total number of green buttons = 7 u + 1 p

7 u + 1 p = 75 + 396
7 u + 1 p = 471 

1 p = 471 - 7 u --- (1)

Total number of gold buttons = 3 u + 1 p
3 u + 1 p = 175 + 264
3 u + 1 p = 439

1 p = 439 - 3 u --- (2)

(2) = (1)
439 - 3 u = 471 - 7 u
7 u - 3 u = 471 - 439
4 u = 32

1 u = 32 ÷ 4 = 8

Total number of gold buttons and green buttons that must be moved from Box Q to Box R
= 250 - 10 u
= 250 - 10 x 8
= 250 - 80
= 170

Answer(s): 170