Container S contains 7 purple beads and 12 gold beads. Container T contains 62 purple beads and 18 gold beads. How many gold beads and purple beads must be moved from Container T to put into Container S so that 50% of the beads in Container A are purple and 80% of the beads in Container T are purple?

	Container S		Container T
	Purple beads	Gold beads	Purple beads	Gold beads
Before	7	12	62	18
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	4 p	1 p

50% = ⁵⁰₁₀₀ = 12

80% = ⁸⁰₁₀₀ = 45

Number of purple beads = 7 + 62 = 69 

Number of gold beads = 12 + 18 = 30 

1 u + 4 p = 69 --- (1)

1 u + 1 p = 30 ---(2)

(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 69 - 30
4 p - 1 p = 39
3 p = 39

1 p = 39 ÷ 3 = 13

From (2):
1 u + 1 p = 30
1 u + 1 x 13 = 30
1 u + 13 = 30

1 u = 30 - 13 = 17

Number of gold beads to be moved from Container T to Container S
= 18 - 1 p
= 18 - 1 x 13
= 18 - 13
= 5

Number of purple beads to be moved from Container T to Container S
= 1 u - 7
= 17 - 7
= 10

Total number of gold and purple beads to be moved from Container T to Container S
= 5 + 10
= 15

Answer(s): 15