Marion had four boxes, U, V, W and X which contained a total of 278 oranges. She transferred 13 oranges from Box U to Box V, 33 oranges from Box V to Box W and 63 oranges from Box W to Box X. The ratio of the number of oranges in Box U to Box V to Box W changed from  2 : 6 : 9 to 1 : 4 : 6. How many oranges were in Box X at first?

	Make p the same (1)x4 = (3)	U (1)	V (2)	W	X
Before	8 u	2 u	6 u	9 u	?
Change 1	- 52	- 13	+ 13
Change 2			- 33	+ 33
Change 3				- 63	+ 63
After	4 p	1 p	4 p	6 p	?

2 u - 13 = 1 p --- (1)

6 u + 13 - 33 = 4 p
6 u - 20 = 4 p --- (2)

(1) _{x 4}
8 u - 52 = 4 p --- (3)

Make p the same.

(3) = (2)
8 u - 52 = 6 u - 20
8 u - 6 u = 52 - 20
2 u = 32

1 u = 32 ÷ 2 = 16

Total number of oranges in Box U, Box V and Box W
= 2 u + 6 u + 9 u
= 17 u

Total number of oranges in Box X at first
= 278 - 17 u
= 278 - 17 x 16
= 278 - 272
= 6

Answer(s): 6