There were some yellow marbles and gold marbles. The marbles were packed into 2 bags. At first, Box B contained 200 marbles and 30% of them were gold marbles. Box C contained 208 marbles and 75% of them were gold marbles. How many yellow marbles and gold marbles in total must be moved from Box B to Box C such that 25% of the marbles in Box B are yellow and 50% of the marbles in Box C are gold?

	Box B		Box C
Total	200		208
	Gold marbles	Yellow marbles	Gold marbles	Yellow marbles
Before	60	140	156	52
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of gold marbles in Box B at first
= 30% x 200
= ³⁰₁₀₀ x 200
= 60

Number of yellow marbles in Box B at first
= 200 - 60
= 140

Number of gold marbles in Box C at first
= 75% x 208
= ⁷⁵₁₀₀ x 208
= 156

Number of yellow marbles in Box C at first
= 208 - 156
= 52

Box B in the end
25% = ²⁵₁₀₀ =¹₄
Gold marbles : Yellow marbles = 3 : 1

Box C in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold marbles : Yellow marbles = 1 : 1

Total number of gold marbles = 3 u + 1 p

3 u + 1 p = 60 + 156
3 u + 1 p = 216 

1 p = 216 - 3 u --- (1)

Total number of yellow marbles = 1 u + 1 p
1 u + 1 p = 140 + 52
1 u + 1 p = 192

1 p = 192 - 1 u --- (2)

(2) = (1)
192 - 1 u = 216 - 3 u
3 u - 1 u = 216 - 192
2 u = 24

1 u = 24 ÷ 2 = 12

Total number of yellow marbles and gold marbles that must be moved from Box B to Box C
= 200 - 4 u
= 200 - 4 x 12
= 200 - 48
= 152

Answer(s): 152