At first, Nick, Xandra and Cody had some mini cupcakes in the ratio 8 : 6 : 7 respectively. Nick had 448 mini cupcakes. Then he gave all his mini cupcakes to Xandra and Cody. After receiving the mini cupcakes from Nick, Xandra and Cody had the same number of mini cupcakes. How many mini cupcakes did Xandra receive from Nick?

	Nick	Xandra	Cody	Total
Before	8x2 = 16 u	6x2 = 12 u	7x2 = 14 u	21x2 = 42 u
Change	- 8 u	+ 8 u
After	0	1x21 = 21 u	1x21 = 21 u	2x21 = 42 u

The total number of mini cupcakes remains unchanged. Make the total number of mini cupcakes the same.  LCM of 2 and 21 is 42.

Total number of mini cupcakes = 42 u

Number of mini cupcakes that Xandra had in the end 
= 42 u ÷ 2
= 21 u

Number of mini cupcakes that Nick had at first = 8 u 

8 u = 448

1 u = 448 ÷ 8 = 56

Number of mini cupcakes that Xandra received from Nick
= 21 u - 12 u
= 9 u
= 9 x 56
= 504

Answer(s): 504