Crate Q contains 4 purple beads and 6 pink beads. Crate R contains 39 purple beads and 21 pink beads. How many pink beads and purple beads must be transferred from Crate R to put into Crate Q so that 50% of the beads in Crate A are purple and 75% of the beads in Crate R are purple?

	Crate Q		Crate R
	Purple beads	Pink beads	Purple beads	Pink beads
Before	4	6	39	21
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of purple beads = 4 + 39 = 43 

Number of pink beads = 6 + 21 = 27 

1 u + 3 p = 43 --- (1)

1 u + 1 p = 27 ---(2)

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 43 - 27
3 p - 1 p = 16
2 p = 16

1 p = 16 ÷ 2 = 8

From (2):
1 u + 1 p = 27
1 u + 1 x 8 = 27
1 u + 8 = 27

1 u = 27 - 8 = 19

Number of pink beads to be transferred from Crate R to Crate Q
= 21 - 1 p
= 21 - 1 x 8
= 21 - 8
= 13

Number of purple beads to be transferred from Crate R to Crate Q
= 1 u - 4
= 19 - 4
= 15

Total number of pink and purple beads to be transferred from Crate R to Crate Q
= 13 + 15
= 28

Answer(s): 28