At first, Ethan, Kylie and Elijah had some mochi balls in the ratio 8 : 6 : 7 respectively. Ethan had 336 mochi balls. Then he gave all his mochi balls to Kylie and Elijah. After receiving the mochi balls from Ethan, Kylie and Elijah had the same number of mochi balls. How many mochi balls did Kylie receive from Ethan?

	Ethan	Kylie	Elijah	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 Kylie had in the end 
= 42 u ÷ 2
= 21 u

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

8 u = 336

1 u = 336 ÷ 8 = 42

Number of mochi balls that Kylie received from Ethan
= 21 u - 12 u
= 9 u
= 9 x 42
= 378

Answer(s): 378