At first, Michael, Hilda and Fabian had some mochi balls in the ratio 8 : 6 : 7 respectively. Michael had 432 mochi balls. Then he gave all his mochi balls to Hilda and Fabian. After receiving the mochi balls from Michael, Hilda and Fabian had the same number of mochi balls. How many mochi balls did Hilda receive from Michael?

	Michael	Hilda	Fabian	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 mochi balls remains unchanged. Make the total number of mochi balls the same.  LCM of 2 and 21 is 42.

Total number of mochi balls = 42 u

Number of mochi balls that Hilda had in the end 
= 42 u ÷ 2
= 21 u

Number of mochi balls that Michael had at first = 8 u 

8 u = 432

1 u = 432 ÷ 8 = 54

Number of mochi balls that Hilda received from Michael
= 21 u - 12 u
= 9 u
= 9 x 54
= 486

Answer(s): 486