Luke and Luis shared some stamps in the ratio of 5 : 7. After both each gave away 99 stamps to their cousin, the ratio of the number of stamps Luke had to the total number of stamps left was 1 : 6. How many stamps did the two boys have in the end?

	Luke	Luis	Difference
Before	5x2 = 10 u	7x2 = 14 u	2x2 = 4 u
Change	- 99	- 99
After	1x1 = 1 u	5x1 = 5 u	4x1 = 4 u

Number of stamps that Luke and Luis each gave to their cousin is the same.

The difference in the number of stamps at first and in the end between Luke and Luis remains unchanged.  Make the difference in the number of stamps the same.  LCM of 2 and 4 is 4.

Number of stamps that Luke gave to their cousin
= 10 u - 1 u
= 9 u

9 u = 99

1 u = 99 ÷ 9 = 11

Number of stamps that the two boys had in the end
= 1 u + 5 u
= 6 u
= 6 x 11
= 66

Answer(s): 66