Kathy had four boxes, W, X, Y and Z which contained a total of 316 pomegranates. She transferred 22 pomegranates from Box W to Box X, 38 pomegranates from Box X to Box Y and 48 pomegranates from Box Y to Box Z. The ratio of the number of pomegranates in Box W to Box X to Box Y changed from  4 : 7 : 10 to 1 : 4 : 7. How many pomegranates were in Box Z at first?

	Make p the same (1)x4 = (3)	W (1)	X (2)	Y	Z
Before	16 u	4 u	7 u	10 u	?
Change 1	- 88	- 22	+ 22
Change 2			- 38	+ 38
Change 3				- 48	+ 48
After	4 p	1 p	4 p	7 p	?

4 u - 22 = 1 p --- (1)

7 u + 22 - 38 = 4 p
7 u - 16 = 4 p --- (2)

(1) _{x 4}
16 u - 88 = 4 p --- (3)

Make p the same.

(3) = (2)
16 u - 88 = 7 u - 16
16 u - 7 u = 88 - 16
9 u = 72

1 u = 72 ÷ 9 = 8

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

Total number of pomegranates in Box Z at first
= 316 - 21 u
= 316 - 21 x 8
= 316 - 168
= 148

Answer(s): 148