Opal had four boxes, G, H, J and K which contained a total of 334 persimmons. She transferred 28 persimmons from Box G to Box H, 67 persimmons from Box H to Box J and 139 persimmons from Box J to Box K. The ratio of the number of persimmons in Box G to Box H to Box J changed from  2 : 3 : 6 to 1 : 3 : 9. How many persimmons were in Box K at first?

	Make p the same (1)x3 = (3)	G (1)	H (2)	J	K
Before	6 u	2 u	3 u	6 u	?
Change 1	- 84	- 28	+ 28
Change 2			- 67	+ 67
Change 3				- 139	+ 139
After	3 p	1 p	3 p	9 p	?

2 u - 28 = 1 p --- (1)

3 u + 28 - 67 = 3 p
3 u - 39 = 3 p --- (2)

(1) _{x 3}
6 u - 84 = 3 p --- (3)

Make p the same.

(3) = (2)
6 u - 84 = 3 u - 39
6 u - 3 u = 84 - 39
3 u = 45

1 u = 45 ÷ 3 = 15

Total number of persimmons in Box G, Box H and Box J
= 2 u + 3 u + 6 u
= 11 u

Total number of persimmons in Box K at first
= 334 - 11 u
= 334 - 11 x 15
= 334 - 165
= 169

Answer(s): 169