Crate K contains 6 black balls and 7 gold balls. Crate L contains 31 black balls and 18 gold balls. How many gold balls and black balls must be moved from Crate L to put into Crate K so that 50% of the balls in Crate A are black and 75% of the balls in Crate L are black?

	Crate K		Crate L
	Black balls	Gold balls	Black balls	Gold balls
Before	6	7	31	18
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of black balls = 6 + 31 = 37 

Number of gold balls = 7 + 18 = 25 

1 u + 3 p = 37 --- (1)

1 u + 1 p = 25 ---(2)

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 37 - 25
3 p - 1 p = 12
2 p = 12

1 p = 12 ÷ 2 = 6

From (2):
1 u + 1 p = 25
1 u + 1 x 6 = 25
1 u + 6 = 25

1 u = 25 - 6 = 19

Number of gold balls to be moved from Crate L to Crate K
= 18 - 1 p
= 18 - 1 x 6
= 18 - 6
= 12

Number of black balls to be moved from Crate L to Crate K
= 1 u - 6
= 19 - 6
= 13

Total number of gold and black balls to be moved from Crate L to Crate K
= 12 + 13
= 25

Answer(s): 25