There were some yellow pens and grey pens. The pens were packed into 2 bags. At first, Bag R contained 270 pens and 30% of them were grey pens. Bag S contained 600 pens and 60% of them were grey pens. How many yellow pens and grey pens in total must be moved from Bag R to Bag S such that 25% of the pens in Bag R are yellow and 50% of the pens in Bag S are grey?

	Bag R		Bag S
Total	270		600
	Grey pens	Yellow pens	Grey pens	Yellow pens
Before	81	189	360	240
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of grey pens in Bag R at first
= 30% x 270
= ³⁰₁₀₀ x 270
= 81

Number of yellow pens in Bag R at first
= 270 - 81
= 189

Number of grey pens in Bag S at first
= 60% x 600
= ⁶⁰₁₀₀ x 600
= 360

Number of yellow pens in Bag S at first
= 600 - 360
= 240

Bag R in the end
25% = ²⁵₁₀₀ =¹₄
Grey pens : Yellow pens = 3 : 1

Bag S in the end
50% = ⁵⁰₁₀₀ =¹₂
Grey pens : Yellow pens = 1 : 1

Total number of grey pens = 3 u + 1 p

3 u + 1 p = 81 + 360
3 u + 1 p = 441 

1 p = 441 - 3 u --- (1)

Total number of yellow pens = 1 u + 1 p
1 u + 1 p = 189 + 240
1 u + 1 p = 429

1 p = 429 - 1 u --- (2)

(2) = (1)
429 - 1 u = 441 - 3 u
3 u - 1 u = 441 - 429
2 u = 12

1 u = 12 ÷ 2 = 6

Total number of yellow pens and grey pens that must be moved from Bag R to Bag S
= 270 - 4 u
= 270 - 4 x 6
= 270 - 24
= 246

Answer(s): 246