Crate Y contains 2 purple beads and 9 white beads. Crate Z contains 89 purple beads and 25 white beads. How many white beads and purple beads must be transferred from Crate Z to put into Crate Y so that 50% of the beads in Crate A are purple and 80% of the beads in Crate Z are purple?

	Crate Y		Crate Z
	Purple beads	White beads	Purple beads	White beads
Before	2	9	89	25
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	4 p	1 p

50% = ⁵⁰₁₀₀ = 12

80% = ⁸⁰₁₀₀ = 45

Number of purple beads = 2 + 89 = 91 

Number of white beads = 9 + 25 = 34 

1 u + 4 p = 91 --- (1)

1 u + 1 p = 34 ---(2)

(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 91 - 34
4 p - 1 p = 57
3 p = 57

1 p = 57 ÷ 3 = 19

From (2):
1 u + 1 p = 34
1 u + 1 x 19 = 34
1 u + 19 = 34

1 u = 34 - 19 = 15

Number of white beads to be transferred from Crate Z to Crate Y
= 25 - 1 p
= 25 - 1 x 19
= 25 - 19
= 6

Number of purple beads to be transferred from Crate Z to Crate Y
= 1 u - 2
= 15 - 2
= 13

Total number of white and purple beads to be transferred from Crate Z to Crate Y
= 6 + 13
= 19

Answer(s): 19