There were red, yellow and gold marbles in a container. Sean put another 3 red marbles and 5 gold marbles in the container, then the ratio of the number of yellow marbles to the number of gold marbles became 5 : 3. Then, he doubled the number of red marbles and removed 30 gold marbles. The ratio of the number of red marbles to yellow marbles became 2 : 1. He counted and found that there were a total of 114 marbles left in the container. Find the number of red marbles that he had in the end.

	Red marbles	Yellow marbles	Gold marbles	Total
Before	5 u - 3	5 u	3 u - 5
Change 1	+ 3		+ 5
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 30
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 30	114

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

Total number of marbles in the end
= 10 u + 5 u + 3 u - 30
= 18 u - 30

18 u - 30 = 114
18 u = 114 + 30
18 u = 144

1 u = 144 ÷ 18 = 8

Number of red marbles in the end
= 10 u 
= 10 x 8
= 80

Answer(s): 80