At first, Ian, Gwen and Sam had some candy canes in the ratio 7 : 5 : 6 respectively. Ian had 238 candy canes. Then he gave all his candy canes to Gwen and Sam. After receiving the candy canes from Ian, Gwen and Sam had the same number of candy canes. How many candy canes did Gwen receive from Ian?

	Ian	Gwen	Sam	Total
Before	7x1 = 7 u	5x1 = 5 u	6x1 = 6 u	18x1 = 18 u
Change	- 7 u	+ 7 u
After	0	1x9 = 9 u	1x9 = 9 u	2x9 = 18 u

The total number of candy canes remains unchanged. Make the total number of candy canes the same.  LCM of 2 and 18 is 18.

Total number of candy canes = 18 u

Number of candy canes that Gwen had in the end 
= 18 u ÷ 2
= 9 u

Number of candy canes that Ian had at first = 7 u 

7 u = 238

1 u = 238 ÷ 7 = 34

Number of candy canes that Gwen received from Ian
= 9 u - 5 u
= 4 u
= 4 x 34
= 136

Answer(s): 136