Will, David and Tommy had a total of 109 coins. The ratio of David's coins to Tommy's coins was 2 : 9 at first. Will and David each gave away ¹₂ of their coins. Given that the three boys had 95 coins left, how many coins did Will have at first?

	Will	David	Tommy	Total
Comparing David and Tommy at first		2 u	9 u
Before	2 p	2x1 = 2 u	9 u	109
Change	- 1 p	-1x1 = - 1 u		- 14
After	1 p	1x1 = 1 u	9 u	95

Total number of coins that Will and David gave away
= 109 - 95
= 14

The number of coins that David had at first is repeated.  Make the number of coins that David had at first the same.  LCM of 2 and 2 is 2.

1 p + 1 u = 109 - 95
1 p + 1 u = 14
1 p = 14 - 1 u --- (1)

1 p + 1 u + 9 u = 95
1 p + 10 u = 95
1 p = 95 - 10 u --- (2)

(1) = (2)
14 - 1 u = 95 - 10 u
10 u - 1 u = 95 - 14
10 u - 1 u = 81
9 u = 81

1 u = 81 ÷ 9 = 9

Substitute 1 u = 9 into (1).
1 p = 14 - 1 u
1 p = 14 - 1 x 9
1 p = 14 - 9

1 p = 5

Number of coins that Will had at first
= 2 p
= 2 x 5
= 10

Answer(s): 10