There were red, brown and white marbles in a bottle. Sean put another 8 red marbles and 12 white marbles in the bottle, then the ratio of the number of brown marbles to the number of white marbles became 5 : 2. Then, he doubled the number of red marbles and removed 19 white 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 100 marbles left in the bottle. Find the number of red marbles that he had at first.

	Red marbles	Brown marbles	White marbles	Total
Before	5 u - 8	5 u	2 u - 12
Change 1	+ 8		+ 12
After 1	1x5 = 5 u	5 u	2 u
Change 2	+ 1x5 = 5 u		- 19
After 2	2x5 = 10 u	1x5 = 5 u	2 u - 19	100

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 + 2 u - 19
= 17 u - 19

17 u - 19 = 100
17 u = 100 + 19
17 u = 119

1 u = 119 ÷ 17 = 7

Number of red marbles at first
= 5 u - 8
= 5 x 7 - 8
= 35 - 8
= 27

Answer(s): 27