There were some pink marbles and silver marbles. The marbles were packed into 2 bags. At first, Box B contained 80 marbles and 40% of them were silver marbles. Box C contained 40 marbles and 80% of them were silver marbles. How many pink marbles and silver marbles in total must be moved from Box B to Box C such that 30% of the marbles in Box B are pink and 50% of the marbles in Box C are silver?

	Box B		Box C
Total	80		40
	Silver marbles	Pink marbles	Silver marbles	Pink marbles
Before	32	48	32	8
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of silver marbles in Box B at first
= 40% x 80
= ⁴⁰₁₀₀ x 80
= 32

Number of pink marbles in Box B at first
= 80 - 32
= 48

Number of silver marbles in Box C at first
= 80% x 40
= ⁸⁰₁₀₀ x 40
= 32

Number of pink marbles in Box C at first
= 40 - 32
= 8

Box B in the end
30% = ³⁰₁₀₀ =³₁₀
Silver marbles : Pink marbles = 7 : 3

Box C in the end
50% = ⁵⁰₁₀₀ =¹₂
Silver marbles : Pink marbles = 1 : 1

Total number of silver marbles = 7 u + 1 p

7 u + 1 p = 32 + 32
7 u + 1 p = 64 

1 p = 64 - 7 u --- (1)

Total number of pink marbles = 3 u + 1 p
3 u + 1 p = 48 + 8
3 u + 1 p = 56

1 p = 56 - 3 u --- (2)

(2) = (1)
56 - 3 u = 64 - 7 u
7 u - 3 u = 64 - 56
4 u = 8

1 u = 8 ÷ 4 = 2

Total number of pink marbles and silver marbles that must be moved from Box B to Box C
= 80 - 10 u
= 80 - 10 x 2
= 80 - 20
= 60

Answer(s): 60