There were white, green and purple beads in a container. Sean put another 9 white beads and 4 purple beads in the container, then the ratio of the number of green beads to the number of purple beads became 4 : 3. Then, he doubled the number of white beads and removed 14 purple beads. The ratio of the number of white beads to green beads became 2 : 1. He counted and found that there were a total of 61 beads left in the container. Find the number of white beads that he had in the end.

	White beads	Green beads	Purple beads	Total
Before	4 u - 9	4 u	3 u - 4
Change 1	+ 9		+ 4
After 1	1x4 = 4 u	4 u	3 u
Change 2	+ 1x4 = 4 u		- 14
After 2	2x4 = 8 u	1x4 = 4 u	3 u - 14	61

The number of green beads remains unchanged. Make the number of green beads the same. LCM of 1 and 4 is 4.

Total number of beads in the end
= 8 u + 4 u + 3 u - 14
= 15 u - 14

15 u - 14 = 61
15 u = 61 + 14
15 u = 75

1 u = 75 ÷ 15 = 5

Number of white beads in the end
= 8 u 
= 8 x 5
= 40

Answer(s): 40