There were red, brown and gold marbles in a container. Sean put another 3 red marbles and 2 gold marbles in the container, then the ratio of the number of brown marbles to the number of gold marbles became 5 : 3. Then, he doubled the number of red marbles and removed 11 gold marbles. The ratio of the number of red marbles to brown marbles became 2 : 1. He counted and found that there were a total of 79 marbles left in the container. Find the number of red marbles that he had at first.

	Red marbles	Brown marbles	Gold marbles	Total
Before	5 u - 3	5 u	3 u - 2
Change 1	+ 3		+ 2
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 11
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 11	79

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

Total number of marbles in the end
= 10 u + 5 u + 3 u - 11
= 18 u - 11

18 u - 11 = 79
18 u = 79 + 11
18 u = 90

1 u = 90 ÷ 18 = 5

Number of red marbles at first
= 5 u - 3
= 5 x 5 - 3
= 25 - 3
= 22

Answer(s): 22