Crate A contains 15 purple marbles and 9 green marbles. Crate B contains 40 purple marbles and 19 green marbles. How many green marbles and purple marbles must be transferred from Crate B to put into Crate A so that 50% of the marbles in Crate A are purple and 80% of the marbles in Crate B are purple?

	Crate A		Crate B
	Purple marbles	Green marbles	Purple marbles	Green marbles
Before	15	9	40	19
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	4 p	1 p

50% = ⁵⁰₁₀₀ = 12

80% = ⁸⁰₁₀₀ = 45

Number of purple marbles = 15 + 40 = 55 

Number of green marbles = 9 + 19 = 28 

1 u + 4 p = 55 --- (1)

1 u + 1 p = 28 ---(2)

(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 55 - 28
4 p - 1 p = 27
3 p = 27

1 p = 27 ÷ 3 = 9

From (2):
1 u + 1 p = 28
1 u + 1 x 9 = 28
1 u + 9 = 28

1 u = 28 - 9 = 19

Number of green marbles to be transferred from Crate B to Crate A
= 19 - 1 p
= 19 - 1 x 9
= 19 - 9
= 10

Number of purple marbles to be transferred from Crate B to Crate A
= 1 u - 15
= 19 - 15
= 4

Total number of green and purple marbles to be transferred from Crate B to Crate A
= 10 + 4
= 14

Answer(s): 14