There were some purple pens and yellow pens. The pens were packed into 2 bags. At first, Bag P contained 260 pens and 10% of them were yellow pens. Bag Q contained 444 pens and 75% of them were yellow pens. How many purple pens and yellow pens in total must be moved from Bag P to Bag Q such that 25% of the pens in Bag P are purple and 50% of the pens in Bag Q are yellow?

	Bag P		Bag Q
Total	260		444
	Yellow pens	Purple pens	Yellow pens	Purple pens
Before	26	234	333	111
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of yellow pens in Bag P at first
= 10% x 260
= ¹⁰₁₀₀ x 260
= 26

Number of purple pens in Bag P at first
= 260 - 26
= 234

Number of yellow pens in Bag Q at first
= 75% x 444
= ⁷⁵₁₀₀ x 444
= 333

Number of purple pens in Bag Q at first
= 444 - 333
= 111

Bag P in the end
25% = ²⁵₁₀₀ =¹₄
Yellow pens : Purple pens = 3 : 1

Bag Q in the end
50% = ⁵⁰₁₀₀ =¹₂
Yellow pens : Purple pens = 1 : 1

Total number of yellow pens = 3 u + 1 p

3 u + 1 p = 26 + 333
3 u + 1 p = 359 

1 p = 359 - 3 u --- (1)

Total number of purple pens = 1 u + 1 p
1 u + 1 p = 234 + 111
1 u + 1 p = 345

1 p = 345 - 1 u --- (2)

(2) = (1)
345 - 1 u = 359 - 3 u
3 u - 1 u = 359 - 345
2 u = 14

1 u = 14 ÷ 2 = 7

Total number of purple pens and yellow pens that must be moved from Bag P to Bag Q
= 260 - 4 u
= 260 - 4 x 7
= 260 - 28
= 232

Answer(s): 232