Crate B contains 11 blue marbles and 8 black marbles. Crate C contains 24 blue marbles and 13 black marbles. How many black marbles and blue marbles must be moved from Crate C to put into Crate B so that 50% of the marbles in Crate A are blue and 75% of the marbles in Crate C are blue?

	Crate B		Crate C
	Blue marbles	Black marbles	Blue marbles	Black marbles
Before	11	8	24	13
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of blue marbles = 11 + 24 = 35 

Number of black marbles = 8 + 13 = 21 

1 u + 3 p = 35 --- (1)

1 u + 1 p = 21 ---(2)

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 35 - 21
3 p - 1 p = 14
2 p = 14

1 p = 14 ÷ 2 = 7

From (2):
1 u + 1 p = 21
1 u + 1 x 7 = 21
1 u + 7 = 21

1 u = 21 - 7 = 14

Number of black marbles to be moved from Crate C to Crate B
= 13 - 1 p
= 13 - 1 x 7
= 13 - 7
= 6

Number of blue marbles to be moved from Crate C to Crate B
= 1 u - 11
= 14 - 11
= 3

Total number of black and blue marbles to be moved from Crate C to Crate B
= 6 + 3
= 9

Answer(s): 9