Crate A contains 10 black marbles and 15 brown marbles. Crate B contains 21 black marbles and 8 brown marbles. How many brown marbles and black marbles must be moved from Crate B to put into Crate A so that 50% of the marbles in Crate A are black and 70% of the marbles in Crate B are black?

	Crate A		Crate B
	Black marbles	Brown marbles	Black marbles	Brown marbles
Before	10	15	21	8
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	7 p	3 p

50% = ⁵⁰₁₀₀ = 12

70% = ⁷⁰₁₀₀ = 710

Number of black marbles = 10 + 21 = 31 

Number of brown marbles = 15 + 8 = 23 

1 u + 7 p = 31 --- (1)

1 u + 3 p = 23 ---(2)

(1) - (2)
(1 u + 7 p) - (1 u + 3 p) = 31 - 23
7 p - 3 p = 8
4 p = 8

1 p = 8 ÷ 4 = 2

From (2):
1 u + 3 p = 23
1 u + 3 x 2 = 23
1 u + 6 = 23

1 u = 23 - 6 = 17

Number of brown marbles to be moved from Crate B to Crate A
= 8 - 3 p
= 8 - 3 x 2
= 8 - 6
= 2

Number of black marbles to be moved from Crate B to Crate A
= 1 u - 10
= 17 - 10
= 7

Total number of brown and black marbles to be moved from Crate B to Crate A
= 2 + 7
= 9

Answer(s): 9