Shiyun had four boxes, S, T, U and V which contained a total of 289 mangoes. She transferred 16 mangoes from Box S to Box T, 50 mangoes from Box T to Box U and 103 mangoes from Box U to Box V. The ratio of the number of mangoes in Box S to Box T to Box U changed from  2 : 6 : 11 to 1 : 4 : 8. How many mangoes were in Box V at first?

	Make p the same (1)x4 = (3)	S (1)	T (2)	U	V
Before	8 u	2 u	6 u	11 u	?
Change 1	- 64	- 16	+ 16
Change 2			- 50	+ 50
Change 3				- 103	+ 103
After	4 p	1 p	4 p	8 p	?

2 u - 16 = 1 p --- (1)

6 u + 16 - 50 = 4 p
6 u - 34 = 4 p --- (2)

(1) _{x 4}
8 u - 64 = 4 p --- (3)

Make p the same.

(3) = (2)
8 u - 64 = 6 u - 34
8 u - 6 u = 64 - 34
2 u = 30

1 u = 30 ÷ 2 = 15

Total number of mangoes in Box S, Box T and Box U
= 2 u + 6 u + 11 u
= 19 u

Total number of mangoes in Box V at first
= 289 - 19 u
= 289 - 19 x 15
= 289 - 285
= 4

Answer(s): 4