Xylia had four boxes, U, V, W and X which contained a total of 215 apples. She transferred 17 apples from Box U to Box V, 49 apples from Box V to Box W and 113 apples from Box W to Box X. The ratio of the number of apples in Box U to Box V to Box W changed from  2 : 5 : 10 to 1 : 4 : 8. How many apples were in Box X at first?

	Make p the same (1)x4 = (3)	U (1)	V (2)	W	X
Before	8 u	2 u	5 u	10 u	?
Change 1	- 68	- 17	+ 17
Change 2			- 49	+ 49
Change 3				- 113	+ 113
After	4 p	1 p	4 p	8 p	?

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

5 u + 17 - 49 = 4 p
5 u - 32 = 4 p --- (2)

(1) _{x 4}
8 u - 68 = 4 p --- (3)

Make p the same.

(3) = (2)
8 u - 68 = 5 u - 32
8 u - 5 u = 68 - 32
3 u = 36

1 u = 36 ÷ 3 = 12

Total number of apples in Box U, Box V and Box W
= 2 u + 5 u + 10 u
= 17 u

Total number of apples in Box X at first
= 215 - 17 u
= 215 - 17 x 12
= 215 - 204
= 11

Answer(s): 11