Jack and Reggie shared some pens in the ratio of 4 : 7. After both each gave away 55 pens to their cousin, the ratio of the number of pens Jack had to the total number of pens left was 1 : 4. How many pens did the two boys have in the end?

	Jack	Reggie	Difference
Before	4x2 = 8 u	7x2 = 14 u	3x2 = 6 u
Change	- 55	- 55
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of pens that Jack and Reggie each gave to their cousin is the same.

The difference in the number of pens at first and in the end between Jack and Reggie remains unchanged.  Make the difference in the number of pens the same.  LCM of 3 and 2 is 6.

Number of pens that Jack gave to their cousin
= 8 u - 3 u
= 5 u

5 u = 55

1 u = 55 ÷ 5 = 11

Number of pens that the two boys had in the end
= 3 u + 9 u
= 12 u
= 12 x 11
= 132

Answer(s): 132