There were gold, white and pink beads in a jar. Sean put another 9 gold beads and 7 pink beads in the jar, then the ratio of the number of white beads to the number of pink beads became 5 : 3. Then, he doubled the number of gold beads and removed 29 pink beads. The ratio of the number of gold beads to white beads became 2 : 1. He counted and found that there were a total of 97 beads left in the jar. Find the number of gold beads that he had at first.

	Gold beads	White beads	Pink beads	Total
Before	5 u - 9	5 u	3 u - 7
Change 1	+ 9		+ 7
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 29
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 29	97

The number of white beads remains unchanged. Make the number of white beads the same. LCM of 1 and 5 is 5.

Total number of beads in the end
= 10 u + 5 u + 3 u - 29
= 18 u - 29

18 u - 29 = 97
18 u = 97 + 29
18 u = 126

1 u = 126 ÷ 18 = 7

Number of gold beads at first
= 5 u - 9
= 5 x 7 - 9
= 35 - 9
= 26

Answer(s): 26