Crate E contains 6 black beads and 18 brown beads. Crate F contains 42 black beads and 14 brown beads. How many brown beads and black beads must be moved from Crate F to put into Crate E so that 50% of the beads in Crate A are black and 70% of the beads in Crate F are black?

	Crate E		Crate F
	Black beads	Brown beads	Black beads	Brown beads
Before	6	18	42	14
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	7 p	3 p

50% = ⁵⁰₁₀₀ = 12

70% = ⁷⁰₁₀₀ = 710

Number of black beads = 6 + 42 = 48 

Number of brown beads = 18 + 14 = 32 

1 u + 7 p = 48 --- (1)

1 u + 3 p = 32 ---(2)

(1) - (2)
(1 u + 7 p) - (1 u + 3 p) = 48 - 32
7 p - 3 p = 16
4 p = 16

1 p = 16 ÷ 4 = 4

From (2):
1 u + 3 p = 32
1 u + 3 x 4 = 32
1 u + 12 = 32

1 u = 32 - 12 = 20

Number of brown beads to be moved from Crate F to Crate E
= 14 - 3 p
= 14 - 3 x 4
= 14 - 12
= 2

Number of black beads to be moved from Crate F to Crate E
= 1 u - 6
= 20 - 6
= 14

Total number of brown and black beads to be moved from Crate F to Crate E
= 2 + 14
= 16

Answer(s): 16