Andy, Wesley and Ivan had a total of 116 coins. The ratio of Wesley's coins to Ivan's coins was 6 : 7 at first. Andy and Wesley each gave away ¹₂ of their coins. Given that the three boys had 86 coins left, how many coins did Andy have in the end?

	Andy	Wesley	Ivan	Total
Comparing Wesley and Ivan at first		6 u	7 u
Before	2 p	2x3 = 6 u	7 u	116
Change	- 1 p	-1x3 = - 3 u		- 30
After	1 p	1x3 = 3 u	7 u	86

Total number of coins that Andy and Wesley gave away
= 116 - 86
= 30

The number of coins that Wesley had at first is repeated.  Make the number of coins that Wesley had at first the same.  LCM of 6 and 2 is 6.

1 p + 3 u = 116 - 86
1 p + 3 u = 30
1 p = 30 - 3 u --- (1)

1 p + 3 u + 7 u = 86
1 p + 10 u = 86
1 p = 86 - 10 u --- (2)

(1) = (2)
30 - 3 u = 86 - 10 u
10 u - 3 u = 86 - 30
10 u - 3 u = 56
7 u = 56

1 u = 56 ÷ 7 = 8

Substitute 1 u = 8 into (1).
1 p = 30 - 3 u
1 p = 30 - 3 x 8
1 p = 30 - 24

1 p = 6

Number of coins that Andy had in the end
= 1 p
= 6

Answer(s): 6