Natalie had four containers, F, G, H and J which contained a total of 206 starfruits. She transferred 20 starfruits from Container F to Container G, 42 starfruits from Container G to Container H and 68 starfruits from Container H to Container J. The ratio of the number of starfruits in Container F to Container G to Container H changed from  4 : 7 : 9 to 1 : 5 : 7. How many starfruits were in Container J at first?

	Make p the same (1)x5 = (3)	F (1)	G (2)	H	J
Before	20 u	4 u	7 u	9 u	?
Change 1	- 100	- 20	+ 20
Change 2			- 42	+ 42
Change 3				- 68	+ 68
After	5 p	1 p	5 p	7 p	?

4 u - 20 = 1 p --- (1)

7 u + 20 - 42 = 5 p
7 u - 22 = 5 p --- (2)

(1) _{x 5}
20 u - 100 = 5 p --- (3)

Make p the same.

(3) = (2)
20 u - 100 = 7 u - 22
20 u - 7 u = 100 - 22
13 u = 78

1 u = 78 ÷ 13 = 6

Total number of starfruits in Container F, Container G and Container H
= 4 u + 7 u + 9 u
= 20 u

Total number of starfruits in Container J at first
= 206 - 20 u
= 206 - 20 x 6
= 206 - 120
= 86

Answer(s): 86