Gwen had four boxes, H, J, K and L which contained a total of 230 chikoos. She transferred 19 chikoos from Box H to Box J, 55 chikoos from Box J to Box K and 79 chikoos from Box K to Box L. The ratio of the number of chikoos in Box H to Box J to Box K changed from  3 : 8 : 9 to 1 : 4 : 6. How many chikoos were in Box L at first?

	Make p the same (1)x4 = (3)	H (1)	J (2)	K	L
Before	12 u	3 u	8 u	9 u	?
Change 1	- 76	- 19	+ 19
Change 2			- 55	+ 55
Change 3				- 79	+ 79
After	4 p	1 p	4 p	6 p	?

3 u - 19 = 1 p --- (1)

8 u + 19 - 55 = 4 p
8 u - 36 = 4 p --- (2)

(1) _{x 4}
12 u - 76 = 4 p --- (3)

Make p the same.

(3) = (2)
12 u - 76 = 8 u - 36
12 u - 8 u = 76 - 36
4 u = 40

1 u = 40 ÷ 4 = 10

Total number of chikoos in Box H, Box J and Box K
= 3 u + 8 u + 9 u
= 20 u

Total number of chikoos in Box L at first
= 230 - 20 u
= 230 - 20 x 10
= 230 - 200
= 30

Answer(s): 30