There were white, gold and purple balls in a bottle. Sean put another 9 white balls and 6 purple balls in the bottle, then the ratio of the number of gold balls to the number of purple balls became 5 : 3. Then, he doubled the number of white balls and removed 15 purple balls. The ratio of the number of white balls to gold balls became 2 : 1. He counted and found that there were a total of 39 balls left in the bottle. Find the number of white balls that he had in the end.

	White balls	Gold balls	Purple balls	Total
Before	5 u - 9	5 u	3 u - 6
Change 1	+ 9		+ 6
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 15
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 15	39

The number of gold balls remains unchanged. Make the number of gold balls the same. LCM of 1 and 5 is 5.

Total number of balls in the end
= 10 u + 5 u + 3 u - 15
= 18 u - 15

18 u - 15 = 39
18 u = 39 + 15
18 u = 54

1 u = 54 ÷ 18 = 3

Number of white balls in the end
= 10 u 
= 10 x 3
= 30

Answer(s): 30