Container S contains 9 grey beads and 12 purple beads. Container T contains 70 grey beads and 22 purple beads. How many purple beads and grey beads must be removed from Container T to put into Container S so that 50% of the beads in Container A are grey and 80% of the beads in Container T are grey?

	Container S		Container T
	Grey beads	Purple beads	Grey beads	Purple beads
Before	9	12	70	22
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	4 p	1 p

50% = ⁵⁰₁₀₀ = 12

80% = ⁸⁰₁₀₀ = 45

Number of grey beads = 9 + 70 = 79 

Number of purple beads = 12 + 22 = 34 

1 u + 4 p = 79 --- (1)

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

(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 79 - 34
4 p - 1 p = 45
3 p = 45

1 p = 45 ÷ 3 = 15

From (2):
1 u + 1 p = 34
1 u + 1 x 15 = 34
1 u + 15 = 34

1 u = 34 - 15 = 19

Number of purple beads to be removed from Container T to Container S
= 22 - 1 p
= 22 - 1 x 15
= 22 - 15
= 7

Number of grey beads to be removed from Container T to Container S
= 1 u - 9
= 19 - 9
= 10

Total number of purple and grey beads to be removed from Container T to Container S
= 7 + 10
= 17

Answer(s): 17