Shannon had four boxes, F, G, H and J which contained a total of 282 pomegranates. She transferred 31 pomegranates from Box F to Box G, 57 pomegranates from Box G to Box H and 120 pomegranates from Box H to Box J. The ratio of the number of pomegranates in Box F to Box G to Box H changed from  3 : 5 : 10 to 1 : 4 : 7. How many pomegranates were in Box J at first?

	Make p the same (1)x4 = (3)	F (1)	G (2)	H	J
Before	12 u	3 u	5 u	10 u	?
Change 1	- 124	- 31	+ 31
Change 2			- 57	+ 57
Change 3				- 120	+ 120
After	4 p	1 p	4 p	7 p	?

3 u - 31 = 1 p --- (1)

5 u + 31 - 57 = 4 p
5 u - 26 = 4 p --- (2)

(1) _{x 4}
12 u - 124 = 4 p --- (3)

Make p the same.

(3) = (2)
12 u - 124 = 5 u - 26
12 u - 5 u = 124 - 26
7 u = 98

1 u = 98 ÷ 7 = 14

Total number of pomegranates in Box F, Box G and Box H
= 3 u + 5 u + 10 u
= 18 u

Total number of pomegranates in Box J at first
= 282 - 18 u
= 282 - 18 x 14
= 282 - 252
= 30

Answer(s): 30