Emma had four boxes, V, W, X and Y which contained a total of 249 passion fruits. She transferred 24 passion fruits from Box V to Box W, 40 passion fruits from Box W to Box X and 80 passion fruits from Box X to Box Y. The ratio of the number of passion fruits in Box V to Box W to Box X changed from  4 : 6 : 11 to 1 : 4 : 6. How many passion fruits were in Box Y at first?

	Make p the same (1)x4 = (3)	V (1)	W (2)	X	Y
Before	16 u	4 u	6 u	11 u	?
Change 1	- 96	- 24	+ 24
Change 2			- 40	+ 40
Change 3				- 80	+ 80
After	4 p	1 p	4 p	6 p	?

4 u - 24 = 1 p --- (1)

6 u + 24 - 40 = 4 p
6 u - 16 = 4 p --- (2)

(1) _{x 4}
16 u - 96 = 4 p --- (3)

Make p the same.

(3) = (2)
16 u - 96 = 6 u - 16
16 u - 6 u = 96 - 16
10 u = 80

1 u = 80 ÷ 10 = 8

Total number of passion fruits in Box V, Box W and Box X
= 4 u + 6 u + 11 u
= 21 u

Total number of passion fruits in Box Y at first
= 249 - 21 u
= 249 - 21 x 8
= 249 - 168
= 81

Answer(s): 81