Box N contains 8 white balls and 9 purple balls. Box P contains 36 white balls and 19 purple balls. How many purple balls and white balls must be moved from Box P to put into Box N so that 50% of the balls in Box A are white and 70% of the balls in Box P are white?

	Box N		Box P
	White balls	Purple balls	White balls	Purple balls
Before	8	9	36	19
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	7 p	3 p

50% = ⁵⁰₁₀₀ = 12

70% = ⁷⁰₁₀₀ = 710

Number of white balls = 8 + 36 = 44 

Number of purple balls = 9 + 19 = 28 

1 u + 7 p = 44 --- (1)

1 u + 3 p = 28 ---(2)

(1) - (2)
(1 u + 7 p) - (1 u + 3 p) = 44 - 28
7 p - 3 p = 16
4 p = 16

1 p = 16 ÷ 4 = 4

From (2):
1 u + 3 p = 28
1 u + 3 x 4 = 28
1 u + 12 = 28

1 u = 28 - 12 = 16

Number of purple balls to be moved from Box P to Box N
= 19 - 3 p
= 19 - 3 x 4
= 19 - 12
= 7

Number of white balls to be moved from Box P to Box N
= 1 u - 8
= 16 - 8
= 8

Total number of purple and white balls to be moved from Box P to Box N
= 7 + 8
= 15

Answer(s): 15