Irene had four containers, U, V, W and X which contained a total of 270 oranges. She transferred 16 oranges from Container U to Container V, 28 oranges from Container V to Container W and 32 oranges from Container W to Container X. The ratio of the number of oranges in Container U to Container V to Container W changed from  3 : 5 : 9 to 1 : 3 : 7. How many oranges were in Container X at first?

	Make p the same (1)x3 = (3)	U (1)	V (2)	W	X
Before	9 u	3 u	5 u	9 u	?
Change 1	- 48	- 16	+ 16
Change 2			- 28	+ 28
Change 3				- 32	+ 32
After	3 p	1 p	3 p	7 p	?

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

5 u + 16 - 28 = 3 p
5 u - 12 = 3 p --- (2)

(1) _{x 3}
9 u - 48 = 3 p --- (3)

Make p the same.

(3) = (2)
9 u - 48 = 5 u - 12
9 u - 5 u = 48 - 12
4 u = 36

1 u = 36 ÷ 4 = 9

Total number of oranges in Container U, Container V and Container W
= 3 u + 5 u + 9 u
= 17 u

Total number of oranges in Container X at first
= 270 - 17 u
= 270 - 17 x 9
= 270 - 153
= 117

Answer(s): 117