Seth and Michael shared some pens in the ratio of 5 : 8. After both each gave away 136 pens to their sister, the ratio of the number of pens Seth had to the total number of pens left was 1 : 6. How many pens did the two boys have at first?

	Seth	Michael	Difference
Before	5x4 = 20 u	8x4 = 32 u	3x4 = 12 u
Change	- 136	- 136
After	1x3 = 3 u	5x3 = 15 u	4x3 = 12 u

Number of pens that Seth and Michael each gave to their sister is the same.

The difference in the number of pens at first and in the end between Seth and Michael remains unchanged.  Make the difference in the number of pens the same.  LCM of 3 and 4 is 12.

Number of pens that Seth gave to their sister
= 20 u - 3 u
= 17 u

17 u = 136

1 u = 136 ÷ 17 = 8

Number of pens that the two boys had at first
= 20 u + 32 u
= 52 u
= 52 x 8
= 416

Answer(s): 416