There were some pink pens and white pens. The pens were packed into 2 bags. At first, Bag U contained 260 pens and 30% of them were white pens. Bag V contained 640 pens and 60% of them were white pens. How many pink pens and white pens in total must be moved from Bag U to Bag V such that 20% of the pens in Bag U are pink and 50% of the pens in Bag V are white?

	Bag U		Bag V
Total	260		640
	White pens	Pink pens	White pens	Pink pens
Before	78	182	384	256
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of white pens in Bag U at first
= 30% x 260
= ³⁰₁₀₀ x 260
= 78

Number of pink pens in Bag U at first
= 260 - 78
= 182

Number of white pens in Bag V at first
= 60% x 640
= ⁶⁰₁₀₀ x 640
= 384

Number of pink pens in Bag V at first
= 640 - 384
= 256

Bag U in the end
20% = ²⁰₁₀₀ =¹₅
White pens : Pink pens = 4 : 1

Bag V in the end
50% = ⁵⁰₁₀₀ =¹₂
White pens : Pink pens = 1 : 1

Total number of white pens = 4 u + 1 p

4 u + 1 p = 78 + 384
4 u + 1 p = 462 

1 p = 462 - 4 u --- (1)

Total number of pink pens = 1 u + 1 p
1 u + 1 p = 182 + 256
1 u + 1 p = 438

1 p = 438 - 1 u --- (2)

(2) = (1)
438 - 1 u = 462 - 4 u
4 u - 1 u = 462 - 438
3 u = 24

1 u = 24 ÷ 3 = 8

Total number of pink pens and white pens that must be moved from Bag U to Bag V
= 260 - 5 u
= 260 - 5 x 8
= 260 - 40
= 220

Answer(s): 220