Luke and Tom shared some coins in the ratio of 5 : 7. After both each gave away 143 coins to their brother, the ratio of the number of coins Luke had to the total number of coins left was 1 : 5. How many coins did the two boys have at first?

	Luke	Tom	Difference
Before	5x3 = 15 u	7x3 = 21 u	2x3 = 6 u
Change	- 143	- 143
After	1x2 = 2 u	4x2 = 8 u	3x2 = 6 u

Number of coins that Luke and Tom each gave to their brother is the same.

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

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

13 u = 143

1 u = 143 ÷ 13 = 11

Number of coins that the two boys had at first
= 15 u + 21 u
= 36 u
= 36 x 11
= 396

Answer(s): 396