There were some brown buttons and pink buttons. The buttons were packed into 2 bags. At first, Bag H contained 80 buttons and 40% of them were pink buttons. Bag J contained 44 buttons and 75% of them were pink buttons. How many brown buttons and pink buttons in total must be moved from Bag H to Bag J such that 25% of the buttons in Bag H are brown and 50% of the buttons in Bag J are pink?

	Bag H		Bag J
Total	80		44
	Pink buttons	Brown buttons	Pink buttons	Brown buttons
Before	32	48	33	11
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of pink buttons in Bag H at first
= 40% x 80
= ⁴⁰₁₀₀ x 80
= 32

Number of brown buttons in Bag H at first
= 80 - 32
= 48

Number of pink buttons in Bag J at first
= 75% x 44
= ⁷⁵₁₀₀ x 44
= 33

Number of brown buttons in Bag J at first
= 44 - 33
= 11

Bag H in the end
25% = ²⁵₁₀₀ =¹₄
Pink buttons : Brown buttons = 3 : 1

Bag J in the end
50% = ⁵⁰₁₀₀ =¹₂
Pink buttons : Brown buttons = 1 : 1

Total number of pink buttons = 3 u + 1 p

3 u + 1 p = 32 + 33
3 u + 1 p = 65 

1 p = 65 - 3 u --- (1)

Total number of brown buttons = 1 u + 1 p
1 u + 1 p = 48 + 11
1 u + 1 p = 59

1 p = 59 - 1 u --- (2)

(2) = (1)
59 - 1 u = 65 - 3 u
3 u - 1 u = 65 - 59
2 u = 6

1 u = 6 ÷ 2 = 3

Total number of brown buttons and pink buttons that must be moved from Bag H to Bag J
= 80 - 4 u
= 80 - 4 x 3
= 80 - 12
= 68

Answer(s): 68