Jeremy and Elijah shared some coins in the ratio of 3 : 8. After both each gave away 36 coins to their brother, the ratio of the number of coins Jeremy had to the total number of coins left was 1 : 5. How many coins did the two boys have at first?

	Jeremy	Elijah	Difference
Before	3x3 = 9 u	8x3 = 24 u	5x3 = 15 u
Change	- 36	- 36
After	1x5 = 5 u	4x5 = 20 u	3x5 = 15 u

Number of coins that Jeremy and Elijah each gave to their brother is the same.

The difference in the number of coins at first and in the end between Jeremy and Elijah remains unchanged.  Make the difference in the number of coins the same.  LCM of 5 and 3 is 15.

Number of coins that Jeremy gave to their brother
= 9 u - 5 u
= 4 u

4 u = 36

1 u = 36 ÷ 4 = 9

Number of coins that the two boys had at first
= 9 u + 24 u
= 33 u
= 33 x 9
= 297

Answer(s): 297