Gwen had four boxes, V, W, X and Y which contained a total of 242 oranges. She transferred 36 oranges from Box V to Box W, 90 oranges from Box W to Box X and 166 oranges from Box X to Box Y. The ratio of the number of oranges in Box V to Box W to Box X changed from  4 : 7 : 10 to 1 : 4 : 6. How many oranges were in Box Y at first?

	Make p the same (1)x4 = (3)	V (1)	W (2)	X	Y
Before	16 u	4 u	7 u	10 u	?
Change 1	- 144	- 36	+ 36
Change 2			- 90	+ 90
Change 3				- 166	+ 166
After	4 p	1 p	4 p	6 p	?

4 u - 36 = 1 p --- (1)

7 u + 36 - 90 = 4 p
7 u - 54 = 4 p --- (2)

(1) _{x 4}
16 u - 144 = 4 p --- (3)

Make p the same.

(3) = (2)
16 u - 144 = 7 u - 54
16 u - 7 u = 144 - 54
9 u = 90

1 u = 90 ÷ 9 = 10

Total number of oranges in Box V, Box W and Box X
= 4 u + 7 u + 10 u
= 21 u

Total number of oranges in Box Y at first
= 242 - 21 u
= 242 - 21 x 10
= 242 - 210
= 32

Answer(s): 32