Crate V contains 13 grey balls and 15 purple balls. Crate W contains 68 grey balls and 18 purple balls. How many purple balls and grey balls must be transferred from Crate W to put into Crate V so that 50% of the balls in Crate A are grey and 80% of the balls in Crate W are grey?

	Crate V		Crate W
	Grey balls	Purple balls	Grey balls	Purple balls
Before	13	15	68	18
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	4 p	1 p

50% = ⁵⁰₁₀₀ = 12

80% = ⁸⁰₁₀₀ = 45

Number of grey balls = 13 + 68 = 81 

Number of purple balls = 15 + 18 = 33 

1 u + 4 p = 81 --- (1)

1 u + 1 p = 33 ---(2)

(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 81 - 33
4 p - 1 p = 48
3 p = 48

1 p = 48 ÷ 3 = 16

From (2):
1 u + 1 p = 33
1 u + 1 x 16 = 33
1 u + 16 = 33

1 u = 33 - 16 = 17

Number of purple balls to be transferred from Crate W to Crate V
= 18 - 1 p
= 18 - 1 x 16
= 18 - 16
= 2

Number of grey balls to be transferred from Crate W to Crate V
= 1 u - 13
= 17 - 13
= 4

Total number of purple and grey balls to be transferred from Crate W to Crate V
= 2 + 4
= 6

Answer(s): 6