There were red, brown and pink balls in a jar. Sean put another 2 red balls and 13 pink balls in the jar, then the ratio of the number of brown balls to the number of pink balls became 5 : 3. Then, he doubled the number of red balls and removed 22 pink balls. The ratio of the number of red balls to brown balls became 2 : 1. He counted and found that there were a total of 50 balls left in the jar. Find the number of red balls that he had at first.

	Red balls	Brown balls	Pink balls	Total
Before	5 u - 2	5 u	3 u - 13
Change 1	+ 2		+ 13
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 22
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 22	50

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

Total number of balls in the end
= 10 u + 5 u + 3 u - 22
= 18 u - 22

18 u - 22 = 50
18 u = 50 + 22
18 u = 72

1 u = 72 ÷ 18 = 4

Number of red balls at first
= 5 u - 2
= 5 x 4 - 2
= 20 - 2
= 18

Answer(s): 18