Glen and Japheth shared some coins in the ratio of 5 : 7. After both each gave away 78 coins to their brother, the ratio of the number of coins Glen had to the total number of coins left was 1 : 5. How many coins did the two boys have at first?

	Glen	Japheth	Difference
Before	5x3 = 15 u	7x3 = 21 u	2x3 = 6 u
Change	- 78	- 78
After	1x2 = 2 u	4x2 = 8 u	3x2 = 6 u

Number of coins that Glen and Japheth each gave to their brother is the same.

The difference in the number of coins at first and in the end between Glen and Japheth remains unchanged.  Make the difference in the number of coins the same.  LCM of 2 and 3 is 6.

Number of coins that Glen gave to their brother
= 15 u - 2 u
= 13 u

13 u = 78

1 u = 78 ÷ 13 = 6

Number of coins that the two boys had at first
= 15 u + 21 u
= 36 u
= 36 x 6
= 216

Answer(s): 216