Julian and Peter shared some pens in the ratio of 4 : 7. After both each gave away 143 pens to their brother, the ratio of the number of pens Julian had to the total number of pens left was 1 : 6. How many pens did the two boys have at first?

	Julian	Peter	Difference
Before	4x4 = 16 u	7x4 = 28 u	3x4 = 12 u
Change	- 143	- 143
After	1x3 = 3 u	5x3 = 15 u	4x3 = 12 u

Number of pens that Julian and Peter each gave to their brother is the same.

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

Number of pens that Julian gave to their brother
= 16 u - 3 u
= 13 u

13 u = 143

1 u = 143 ÷ 13 = 11

Number of pens that the two boys had at first
= 16 u + 28 u
= 44 u
= 44 x 11
= 484

Answer(s): 484