Box G contains 11 purple marbles and 2 pink marbles. Box H contains 58 purple marbles and 33 pink marbles. How many pink marbles and purple marbles must be transferred from Box H to put into Box G so that 50% of the marbles in Box A are purple and 75% of the marbles in Box H are purple?

	Box G		Box H
	Purple marbles	Pink marbles	Purple marbles	Pink marbles
Before	11	2	58	33
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of purple marbles = 11 + 58 = 69 

Number of pink marbles = 2 + 33 = 35 

1 u + 3 p = 69 --- (1)

1 u + 1 p = 35 ---(2)

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 69 - 35
3 p - 1 p = 34
2 p = 34

1 p = 34 ÷ 2 = 17

From (2):
1 u + 1 p = 35
1 u + 1 x 17 = 35
1 u + 17 = 35

1 u = 35 - 17 = 18

Number of pink marbles to be transferred from Box H to Box G
= 33 - 1 p
= 33 - 1 x 17
= 33 - 17
= 16

Number of purple marbles to be transferred from Box H to Box G
= 1 u - 11
= 18 - 11
= 7

Total number of pink and purple marbles to be transferred from Box H to Box G
= 16 + 7
= 23

Answer(s): 23