Crate S contains 16 gold beads and 2 red beads. Crate T contains 45 gold beads and 31 red beads. How many red beads and gold beads must be moved from Crate T to put into Crate S so that 50% of the beads in Crate A are gold and 75% of the beads in Crate T are gold?

	Crate S		Crate T
	Gold beads	Red beads	Gold beads	Red beads
Before	16	2	45	31
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of gold beads = 16 + 45 = 61 

Number of red beads = 2 + 31 = 33 

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

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

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 61 - 33
3 p - 1 p = 28
2 p = 28

1 p = 28 ÷ 2 = 14

From (2):
1 u + 1 p = 33
1 u + 1 x 14 = 33
1 u + 14 = 33

1 u = 33 - 14 = 19

Number of red beads to be moved from Crate T to Crate S
= 31 - 1 p
= 31 - 1 x 14
= 31 - 14
= 17

Number of gold beads to be moved from Crate T to Crate S
= 1 u - 16
= 19 - 16
= 3

Total number of red and gold beads to be moved from Crate T to Crate S
= 17 + 3
= 20

Answer(s): 20