Winnie had four boxes, W, X, Y and Z which contained a total of 208 starfruits. She transferred 23 starfruits from Box W to Box X, 52 starfruits from Box X to Box Y and 85 starfruits from Box Y to Box Z. The ratio of the number of starfruits in Box W to Box X to Box Y changed from  4 : 7 : 12 to 1 : 3 : 7. How many starfruits were in Box Z at first?

	Make p the same (1)x3 = (3)	W (1)	X (2)	Y	Z
Before	12 u	4 u	7 u	12 u	?
Change 1	- 69	- 23	+ 23
Change 2			- 52	+ 52
Change 3				- 85	+ 85
After	3 p	1 p	3 p	7 p	?

4 u - 23 = 1 p --- (1)

7 u + 23 - 52 = 3 p
7 u - 29 = 3 p --- (2)

(1) _{x 3}
12 u - 69 = 3 p --- (3)

Make p the same.

(3) = (2)
12 u - 69 = 7 u - 29
12 u - 7 u = 69 - 29
5 u = 40

1 u = 40 ÷ 5 = 8

Total number of starfruits in Box W, Box X and Box Y
= 4 u + 7 u + 12 u
= 23 u

Total number of starfruits in Box Z at first
= 208 - 23 u
= 208 - 23 x 8
= 208 - 184
= 24

Answer(s): 24