There were some purple buttons and pink buttons. The buttons were packed into 2 bags. At first, Box U contained 80 buttons and 40% of them were pink buttons. Box V contained 50 buttons and 80% of them were pink buttons. How many purple buttons and pink buttons in total must be moved from Box U to Box V such that 25% of the buttons in Box U are purple and 50% of the buttons in Box V are pink?

	Box U		Box V
Total	80		50
	Pink buttons	Purple buttons	Pink buttons	Purple buttons
Before	32	48	40	10
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of pink buttons in Box U at first
= 40% x 80
= ⁴⁰₁₀₀ x 80
= 32

Number of purple buttons in Box U at first
= 80 - 32
= 48

Number of pink buttons in Box V at first
= 80% x 50
= ⁸⁰₁₀₀ x 50
= 40

Number of purple buttons in Box V at first
= 50 - 40
= 10

Box U in the end
25% = ²⁵₁₀₀ =¹₄
Pink buttons : Purple buttons = 3 : 1

Box V in the end
50% = ⁵⁰₁₀₀ =¹₂
Pink buttons : Purple buttons = 1 : 1

Total number of pink buttons = 3 u + 1 p

3 u + 1 p = 32 + 40
3 u + 1 p = 72 

1 p = 72 - 3 u --- (1)

Total number of purple buttons = 1 u + 1 p
1 u + 1 p = 48 + 10
1 u + 1 p = 58

1 p = 58 - 1 u --- (2)

(2) = (1)
58 - 1 u = 72 - 3 u
3 u - 1 u = 72 - 58
2 u = 14

1 u = 14 ÷ 2 = 7

Total number of purple buttons and pink buttons that must be moved from Box U to Box V
= 80 - 4 u
= 80 - 4 x 7
= 80 - 28
= 52

Answer(s): 52