Victoria had four containers, C, D, E and F which contained a total of 342 pomegranates. She transferred 24 pomegranates from Container C to Container D, 72 pomegranates from Container D to Container E and 108 pomegranates from Container E to Container F. The ratio of the number of pomegranates in Container C to Container D to Container E changed from  3 : 7 : 12 to 1 : 3 : 9. How many pomegranates were in Container F at first?

	Make p the same (1)x3 = (3)	C (1)	D (2)	E	F
Before	9 u	3 u	7 u	12 u	?
Change 1	- 72	- 24	+ 24
Change 2			- 72	+ 72
Change 3				- 108	+ 108
After	3 p	1 p	3 p	9 p	?

3 u - 24 = 1 p --- (1)

7 u + 24 - 72 = 3 p
7 u - 48 = 3 p --- (2)

(1) _{x 3}
9 u - 72 = 3 p --- (3)

Make p the same.

(3) = (2)
9 u - 72 = 7 u - 48
9 u - 7 u = 72 - 48
2 u = 24

1 u = 24 ÷ 2 = 12

Total number of pomegranates in Container C, Container D and Container E
= 3 u + 7 u + 12 u
= 22 u

Total number of pomegranates in Container F at first
= 342 - 22 u
= 342 - 22 x 12
= 342 - 264
= 78

Answer(s): 78