At first, Mark, Cindy and Ahmad had some mini cupcakes in the ratio 6 : 4 : 5 respectively. Mark had 312 mini cupcakes. Then he gave all his mini cupcakes to Cindy and Ahmad. After receiving the mini cupcakes from Mark, Cindy and Ahmad had the same number of mini cupcakes. How many mini cupcakes did Cindy receive from Mark?

	Mark	Cindy	Ahmad	Total
Before	6x2 = 12 u	4x2 = 8 u	5x2 = 10 u	15x2 = 30 u
Change	- 6 u	+ 6 u
After	0	1x15 = 15 u	1x15 = 15 u	2x15 = 30 u

The total number of mini cupcakes remains unchanged. Make the total number of mini cupcakes the same.  LCM of 2 and 15 is 30.

Total number of mini cupcakes = 30 u

Number of mini cupcakes that Cindy had in the end 
= 30 u ÷ 2
= 15 u

Number of mini cupcakes that Mark had at first = 6 u 

6 u = 312

1 u = 312 ÷ 6 = 52

Number of mini cupcakes that Cindy received from Mark
= 15 u - 8 u
= 7 u
= 7 x 52
= 364

Answer(s): 364