There were some pink marbles and black marbles. The marbles were packed into 2 bags. At first, Bag B contained 200 marbles and 30% of them were black marbles. Bag C contained 490 marbles and 60% of them were black marbles. How many pink marbles and black marbles in total must be moved from Bag B to Bag C such that 25% of the marbles in Bag B are pink and 50% of the marbles in Bag C are black?

	Bag B		Bag C
Total	200		490
	Black marbles	Pink marbles	Black marbles	Pink marbles
Before	60	140	294	196
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of black marbles in Bag B at first
= 30% x 200
= ³⁰₁₀₀ x 200
= 60

Number of pink marbles in Bag B at first
= 200 - 60
= 140

Number of black marbles in Bag C at first
= 60% x 490
= ⁶⁰₁₀₀ x 490
= 294

Number of pink marbles in Bag C at first
= 490 - 294
= 196

Bag B in the end
25% = ²⁵₁₀₀ =¹₄
Black marbles : Pink marbles = 3 : 1

Bag C in the end
50% = ⁵⁰₁₀₀ =¹₂
Black marbles : Pink marbles = 1 : 1

Total number of black marbles = 3 u + 1 p

3 u + 1 p = 60 + 294
3 u + 1 p = 354 

1 p = 354 - 3 u --- (1)

Total number of pink marbles = 1 u + 1 p
1 u + 1 p = 140 + 196
1 u + 1 p = 336

1 p = 336 - 1 u --- (2)

(2) = (1)
336 - 1 u = 354 - 3 u
3 u - 1 u = 354 - 336
2 u = 18

1 u = 18 ÷ 2 = 9

Total number of pink marbles and black marbles that must be moved from Bag B to Bag C
= 200 - 4 u
= 200 - 4 x 9
= 200 - 36
= 164

Answer(s): 164