Bryan, Cody and Zeph had a total of 112 coins. The ratio of Cody's coins to Zeph's coins was 4 : 5 at first. Bryan and Cody each gave away ¹₂ of their coins. Given that the three boys had 86 coins left, how many coins did Bryan have in the end?

	Bryan	Cody	Zeph	Total
Comparing Cody and Zeph at first		4 u	5 u
Before	2 p	2x2 = 4 u	5 u	112
Change	- 1 p	-1x2 = - 2 u		- 26
After	1 p	1x2 = 2 u	5 u	86

Total number of coins that Bryan and Cody gave away
= 112 - 86
= 26

The number of coins that Cody had at first is repeated.  Make the number of coins that Cody had at first the same.  LCM of 4 and 2 is 4.

1 p + 2 u = 112 - 86
1 p + 2 u = 26
1 p = 26 - 2 u --- (1)

1 p + 2 u + 5 u = 86
1 p + 7 u = 86
1 p = 86 - 7 u --- (2)

(1) = (2)
26 - 2 u = 86 - 7 u
7 u - 2 u = 86 - 26
7 u - 2 u = 60
5 u = 60

1 u = 60 ÷ 5 = 12

Substitute 1 u = 12 into (1).
1 p = 26 - 2 u
1 p = 26 - 2 x 12
1 p = 26 - 24

1 p = 2

Number of coins that Bryan had in the end
= 1 p
= 2

Answer(s): 2