At first, Rael, Wendy and Vincent had some mini cupcakes in the ratio 7 : 5 : 6 respectively. Rael had 315 mini cupcakes. Then he gave all his mini cupcakes to Wendy and Vincent. After receiving the mini cupcakes from Rael, Wendy and Vincent had the same number of mini cupcakes. How many mini cupcakes did Wendy receive from Rael?

	Rael	Wendy	Vincent	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 Wendy had in the end 
= 18 u ÷ 2
= 9 u

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

7 u = 315

1 u = 315 ÷ 7 = 45

Number of mini cupcakes that Wendy received from Rael
= 9 u - 5 u
= 4 u
= 4 x 45
= 180

Answer(s): 180