Crate J contains 18 red beads and 8 black beads. Crate K contains 17 red beads and 17 black beads. How many black beads and red beads must be moved from Crate K to put into Crate J so that 50% of the beads in Crate A are red and 75% of the beads in Crate K are red?

	Crate J		Crate K
	Red beads	Black beads	Red beads	Black beads
Before	18	8	17	17
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of red beads = 18 + 17 = 35 

Number of black beads = 8 + 17 = 25 

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

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

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 35 - 25
3 p - 1 p = 10
2 p = 10

1 p = 10 ÷ 2 = 5

From (2):
1 u + 1 p = 25
1 u + 1 x 5 = 25
1 u + 5 = 25

1 u = 25 - 5 = 20

Number of black beads to be moved from Crate K to Crate J
= 17 - 1 p
= 17 - 1 x 5
= 17 - 5
= 12

Number of red beads to be moved from Crate K to Crate J
= 1 u - 18
= 20 - 18
= 2

Total number of black and red beads to be moved from Crate K to Crate J
= 12 + 2
= 14

Answer(s): 14