There were some blue pens and brown pens. The pens were packed into 2 bags. At first, Bag P contained 200 pens and 10% of them were brown pens. Bag Q contained 336 pens and 75% of them were brown pens. How many blue pens and brown pens in total must be moved from Bag P to Bag Q such that 25% of the pens in Bag P are blue and 50% of the pens in Bag Q are brown?

	Bag P		Bag Q
Total	200		336
	Brown pens	Blue pens	Brown pens	Blue pens
Before	20	180	252	84
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of brown pens in Bag P at first
= 10% x 200
= ¹⁰₁₀₀ x 200
= 20

Number of blue pens in Bag P at first
= 200 - 20
= 180

Number of brown pens in Bag Q at first
= 75% x 336
= ⁷⁵₁₀₀ x 336
= 252

Number of blue pens in Bag Q at first
= 336 - 252
= 84

Bag P in the end
25% = ²⁵₁₀₀ =¹₄
Brown pens : Blue pens = 3 : 1

Bag Q in the end
50% = ⁵⁰₁₀₀ =¹₂
Brown pens : Blue pens = 1 : 1

Total number of brown pens = 3 u + 1 p

3 u + 1 p = 20 + 252
3 u + 1 p = 272 

1 p = 272 - 3 u --- (1)

Total number of blue pens = 1 u + 1 p
1 u + 1 p = 180 + 84
1 u + 1 p = 264

1 p = 264 - 1 u --- (2)

(2) = (1)
264 - 1 u = 272 - 3 u
3 u - 1 u = 272 - 264
2 u = 8

1 u = 8 ÷ 2 = 4

Total number of blue pens and brown pens that must be moved from Bag P to Bag Q
= 200 - 4 u
= 200 - 4 x 4
= 200 - 16
= 184

Answer(s): 184