Box F contains 4 brown balls and 6 gold balls. Box G contains 31 brown balls and 17 gold balls. How many gold balls and brown balls must be moved from Box G to put into Box F so that 50% of the balls in Box A are brown and 75% of the balls in Box G are brown?

	Box F		Box G
	Brown balls	Gold balls	Brown balls	Gold balls
Before	4	6	31	17
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	3 p	1 p

50% = ⁵⁰₁₀₀ = 12

75% = ⁷⁵₁₀₀ = 34

Number of brown balls = 4 + 31 = 35 

Number of gold balls = 6 + 17 = 23 

1 u + 3 p = 35 --- (1)

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

(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 35 - 23
3 p - 1 p = 12
2 p = 12

1 p = 12 ÷ 2 = 6

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

1 u = 23 - 6 = 17

Number of gold balls to be moved from Box G to Box F
= 17 - 1 p
= 17 - 1 x 6
= 17 - 6
= 11

Number of brown balls to be moved from Box G to Box F
= 1 u - 4
= 17 - 4
= 13

Total number of gold and brown balls to be moved from Box G to Box F
= 11 + 13
= 24

Answer(s): 24