Container T contains 10 purple beads and 12 gold beads. Container U contains 111 purple beads and 49 gold beads. How many gold beads and purple beads must be transferred from Container U to put into Container T so that 50% of the beads in Container A are purple and 70% of the beads in Container U are purple?

	Container T		Container U
	Purple beads	Gold beads	Purple beads	Gold beads
Before	10	12	111	49
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	7 p	3 p

50% = ⁵⁰₁₀₀ = 12

70% = ⁷⁰₁₀₀ = 710

Number of purple beads = 10 + 111 = 121 

Number of gold beads = 12 + 49 = 61 

1 u + 7 p = 121 --- (1)

1 u + 3 p = 61 ---(2)

(1) - (2)
(1 u + 7 p) - (1 u + 3 p) = 121 - 61
7 p - 3 p = 60
4 p = 60

1 p = 60 ÷ 4 = 15

From (2):
1 u + 3 p = 61
1 u + 3 x 15 = 61
1 u + 45 = 61

1 u = 61 - 45 = 16

Number of gold beads to be transferred from Container U to Container T
= 49 - 3 p
= 49 - 3 x 15
= 49 - 45
= 4

Number of purple beads to be transferred from Container U to Container T
= 1 u - 10
= 16 - 10
= 6

Total number of gold and purple beads to be transferred from Container U to Container T
= 4 + 6
= 10

Answer(s): 10