Crate M contains 8 red beads and 4 purple beads. Crate N contains 47 red beads and 25 purple beads. How many purple beads and red beads must be transferred from Crate N to put into Crate M so that 50% of the beads in Crate A are red and 75% of the beads in Crate N are red?

	Crate M		Crate N
	Red beads	Purple beads	Red beads	Purple beads
Before	8	4	47	25
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of red beads = 8 + 47 = 55 

Number of purple beads = 4 + 25 = 29 

1 u + 3 p = 55 --- (1)

1 u + 1 p = 29 ---(2)

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 55 - 29
3 p - 1 p = 26
2 p = 26

1 p = 26 ÷ 2 = 13

From (2):
1 u + 1 p = 29
1 u + 1 x 13 = 29
1 u + 13 = 29

1 u = 29 - 13 = 16

Number of purple beads to be transferred from Crate N to Crate M
= 25 - 1 p
= 25 - 1 x 13
= 25 - 13
= 12

Number of red beads to be transferred from Crate N to Crate M
= 1 u - 8
= 16 - 8
= 8

Total number of purple and red beads to be transferred from Crate N to Crate M
= 12 + 8
= 20

Answer(s): 20