Cathy had four containers, E, F, G and H which contained a total of 277 pomegranates. She transferred 41 pomegranates from Container E to Container F, 90 pomegranates from Container F to Container G and 190 pomegranates from Container G to Container H. The ratio of the number of pomegranates in Container E to Container F to Container G changed from  4 : 5 : 11 to 1 : 2 : 7. How many pomegranates were in Container H at first?

	Make p the same (1)x2 = (3)	E (1)	F (2)	G	H
Before	8 u	4 u	5 u	11 u	?
Change 1	- 82	- 41	+ 41
Change 2			- 90	+ 90
Change 3				- 190	+ 190
After	2 p	1 p	2 p	7 p	?

4 u - 41 = 1 p --- (1)

5 u + 41 - 90 = 2 p
5 u - 49 = 2 p --- (2)

(1) _{x 2}
8 u - 82 = 2 p --- (3)

Make p the same.

(3) = (2)
8 u - 82 = 5 u - 49
8 u - 5 u = 82 - 49
3 u = 33

1 u = 33 ÷ 3 = 11

Total number of pomegranates in Container E, Container F and Container G
= 4 u + 5 u + 11 u
= 20 u

Total number of pomegranates in Container H at first
= 277 - 20 u
= 277 - 20 x 11
= 277 - 220
= 57

Answer(s): 57