There were some red pens and white pens. The pens were packed into 2 bags. At first, Bag N contained 220 pens and 30% of them were white pens. Bag P contained 208 pens and 75% of them were white pens. How many red pens and white pens in total must be moved from Bag N to Bag P such that 25% of the pens in Bag N are red and 50% of the pens in Bag P are white?

	Bag N		Bag P
Total	220		208
	White pens	Red pens	White pens	Red pens
Before	66	154	156	52
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of white pens in Bag N at first
= 30% x 220
= ³⁰₁₀₀ x 220
= 66

Number of red pens in Bag N at first
= 220 - 66
= 154

Number of white pens in Bag P at first
= 75% x 208
= ⁷⁵₁₀₀ x 208
= 156

Number of red pens in Bag P at first
= 208 - 156
= 52

Bag N in the end
25% = ²⁵₁₀₀ =¹₄
White pens : Red pens = 3 : 1

Bag P in the end
50% = ⁵⁰₁₀₀ =¹₂
White pens : Red pens = 1 : 1

Total number of white pens = 3 u + 1 p

3 u + 1 p = 66 + 156
3 u + 1 p = 222 

1 p = 222 - 3 u --- (1)

Total number of red pens = 1 u + 1 p
1 u + 1 p = 154 + 52
1 u + 1 p = 206

1 p = 206 - 1 u --- (2)

(2) = (1)
206 - 1 u = 222 - 3 u
3 u - 1 u = 222 - 206
2 u = 16

1 u = 16 ÷ 2 = 8

Total number of red pens and white pens that must be moved from Bag N to Bag P
= 220 - 4 u
= 220 - 4 x 8
= 220 - 32
= 188

Answer(s): 188