There were yellow, purple and red marbles in a jar. Sean put another 6 yellow marbles and 12 red marbles in the jar, then the ratio of the number of purple marbles to the number of red marbles became 5 : 3. Then, he doubled the number of yellow marbles and removed 18 red marbles. The ratio of the number of yellow marbles to purple marbles became 2 : 1. He counted and found that there were a total of 90 marbles left in the jar. Find the number of yellow marbles that he had at first.

	Yellow marbles	Purple marbles	Red marbles	Total
Before	5 u - 6	5 u	3 u - 12
Change 1	+ 6		+ 12
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 18
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 18	90

The number of purple marbles remains unchanged. Make the number of purple marbles the same. LCM of 1 and 5 is 5.

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

18 u - 18 = 90
18 u = 90 + 18
18 u = 108

1 u = 108 ÷ 18 = 6

Number of yellow marbles at first
= 5 u - 6
= 5 x 6 - 6
= 30 - 6
= 24

Answer(s): 24