Box U contains 4 red balls and 9 grey balls. Box V contains 85 red balls and 23 grey balls. How many grey balls and red balls must be moved from Box V to put into Box U so that 50% of the balls in Box A are red and 80% of the balls in Box V are red?

	Box U		Box V
	Red balls	Grey balls	Red balls	Grey balls
Before	4	9	85	23
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	4 p	1 p

50% = ⁵⁰₁₀₀ = 12

80% = ⁸⁰₁₀₀ = 45

Number of red balls = 4 + 85 = 89 

Number of grey balls = 9 + 23 = 32 

1 u + 4 p = 89 --- (1)

1 u + 1 p = 32 ---(2)

(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 89 - 32
4 p - 1 p = 57
3 p = 57

1 p = 57 ÷ 3 = 19

From (2):
1 u + 1 p = 32
1 u + 1 x 19 = 32
1 u + 19 = 32

1 u = 32 - 19 = 13

Number of grey balls to be moved from Box V to Box U
= 23 - 1 p
= 23 - 1 x 19
= 23 - 19
= 4

Number of red balls to be moved from Box V to Box U
= 1 u - 4
= 13 - 4
= 9

Total number of grey and red balls to be moved from Box V to Box U
= 4 + 9
= 13

Answer(s): 13