Tiffany had four boxes, A, B, C and D which contained a total of 345 pomegranates. She transferred 41 pomegranates from Box A to Box B, 80 pomegranates from Box B to Box C and 132 pomegranates from Box C to Box D. The ratio of the number of pomegranates in Box A to Box B to Box C changed from  4 : 5 : 9 to 1 : 3 : 8. How many pomegranates were in Box D at first?

	Make p the same (1)x3 = (3)	A (1)	B (2)	C	D
Before	12 u	4 u	5 u	9 u	?
Change 1	- 123	- 41	+ 41
Change 2			- 80	+ 80
Change 3				- 132	+ 132
After	3 p	1 p	3 p	8 p	?

4 u - 41 = 1 p --- (1)

5 u + 41 - 80 = 3 p
5 u - 39 = 3 p --- (2)

(1) _{x 3}
12 u - 123 = 3 p --- (3)

Make p the same.

(3) = (2)
12 u - 123 = 5 u - 39
12 u - 5 u = 123 - 39
7 u = 84

1 u = 84 ÷ 7 = 12

Total number of pomegranates in Box A, Box B and Box C
= 4 u + 5 u + 9 u
= 18 u

Total number of pomegranates in Box D at first
= 345 - 18 u
= 345 - 18 x 12
= 345 - 216
= 129

Answer(s): 129