At first, Julian, Risa and Sam had some mini cupcakes in the ratio 7 : 5 : 6 respectively. Julian had 343 mini cupcakes. Then he gave all his mini cupcakes to Risa and Sam. After receiving the mini cupcakes from Julian, Risa and Sam had the same number of mini cupcakes. How many mini cupcakes did Risa receive from Julian?

	Julian	Risa	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 mini cupcakes remains unchanged. Make the total number of mini cupcakes the same.  LCM of 2 and 18 is 18.

Total number of mini cupcakes = 18 u

Number of mini cupcakes that Risa had in the end 
= 18 u ÷ 2
= 9 u

Number of mini cupcakes that Julian had at first = 7 u 

7 u = 343

1 u = 343 ÷ 7 = 49

Number of mini cupcakes that Risa received from Julian
= 9 u - 5 u
= 4 u
= 4 x 49
= 196

Answer(s): 196