Gem had four boxes, H, J, K and L which contained a total of 238 mangoes. She transferred 17 mangoes from Box H to Box J, 50 mangoes from Box J to Box K and 41 mangoes from Box K to Box L. The ratio of the number of mangoes in Box H to Box J to Box K changed from  3 : 7 : 9 to 1 : 3 : 9. How many mangoes were in Box L at first?

	Make p the same (1)x3 = (3)	H (1)	J (2)	K	L
Before	9 u	3 u	7 u	9 u	?
Change 1	- 51	- 17	+ 17
Change 2			- 50	+ 50
Change 3				- 41	+ 41
After	3 p	1 p	3 p	9 p	?

3 u - 17 = 1 p --- (1)

7 u + 17 - 50 = 3 p
7 u - 33 = 3 p --- (2)

(1) _{x 3}
9 u - 51 = 3 p --- (3)

Make p the same.

(3) = (2)
9 u - 51 = 7 u - 33
9 u - 7 u = 51 - 33
2 u = 18

1 u = 18 ÷ 2 = 9

Total number of mangoes in Box H, Box J and Box K
= 3 u + 7 u + 9 u
= 19 u

Total number of mangoes in Box L at first
= 238 - 19 u
= 238 - 19 x 9
= 238 - 171
= 67

Answer(s): 67