Ian and Brandon shared some marbles in the ratio of 5 : 8. After both each gave away 84 marbles to their cousin, the ratio of the number of marbles Ian had to the total number of marbles left was 1 : 4. How many marbles did the two boys have in the end?

	Ian	Brandon	Difference
Before	5x2 = 10 u	8x2 = 16 u	3x2 = 6 u
Change	- 84	- 84
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of marbles that Ian and Brandon each gave to their cousin is the same.

The difference in the number of marbles at first and in the end between Ian and Brandon remains unchanged.  Make the difference in the number of marbles the same.  LCM of 3 and 2 is 6.

Number of marbles that Ian gave to their cousin
= 10 u - 3 u
= 7 u

7 u = 84

1 u = 84 ÷ 7 = 12

Number of marbles that the two boys had in the end
= 3 u + 9 u
= 12 u
= 12 x 12
= 144

Answer(s): 144