There were some yellow pens and red pens. The pens were packed into 2 bags. At first, Box U contained 280 pens and 10% of them were red pens. Box V contained 1150 pens and 60% of them were red pens. How many yellow pens and red pens in total must be moved from Box U to Box V such that 25% of the pens in Box U are yellow and 50% of the pens in Box V are red?

	Box U		Box V
Total	280		1150
	Red pens	Yellow pens	Red pens	Yellow pens
Before	28	252	690	460
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of red pens in Box U at first
= 10% x 280
= ¹⁰₁₀₀ x 280
= 28

Number of yellow pens in Box U at first
= 280 - 28
= 252

Number of red pens in Box V at first
= 60% x 1150
= ⁶⁰₁₀₀ x 1150
= 690

Number of yellow pens in Box V at first
= 1150 - 690
= 460

Box U in the end
25% = ²⁵₁₀₀ =¹₄
Red pens : Yellow pens = 3 : 1

Box V in the end
50% = ⁵⁰₁₀₀ =¹₂
Red pens : Yellow pens = 1 : 1

Total number of red pens = 3 u + 1 p

3 u + 1 p = 28 + 690
3 u + 1 p = 718 

1 p = 718 - 3 u --- (1)

Total number of yellow pens = 1 u + 1 p
1 u + 1 p = 252 + 460
1 u + 1 p = 712

1 p = 712 - 1 u --- (2)

(2) = (1)
712 - 1 u = 718 - 3 u
3 u - 1 u = 718 - 712
2 u = 6

1 u = 6 ÷ 2 = 3

Total number of yellow pens and red pens that must be moved from Box U to Box V
= 280 - 4 u
= 280 - 4 x 3
= 280 - 12
= 268

Answer(s): 268