Betty had four boxes, S, T, U and V which contained a total of 346 apples. She transferred 27 apples from Box S to Box T, 52 apples from Box T to Box U and 73 apples from Box U to Box V. The ratio of the number of apples in Box S to Box T to Box U changed from  3 : 5 : 9 to 1 : 3 : 7. How many apples were in Box V at first?

	Make p the same (1)x3 = (3)	S (1)	T (2)	U	V
Before	9 u	3 u	5 u	9 u	?
Change 1	- 81	- 27	+ 27
Change 2			- 52	+ 52
Change 3				- 73	+ 73
After	3 p	1 p	3 p	7 p	?

3 u - 27 = 1 p --- (1)

5 u + 27 - 52 = 3 p
5 u - 25 = 3 p --- (2)

(1) _{x 3}
9 u - 81 = 3 p --- (3)

Make p the same.

(3) = (2)
9 u - 81 = 5 u - 25
9 u - 5 u = 81 - 25
4 u = 56

1 u = 56 ÷ 4 = 14

Total number of apples in Box S, Box T and Box U
= 3 u + 5 u + 9 u
= 17 u

Total number of apples in Box V at first
= 346 - 17 u
= 346 - 17 x 14
= 346 - 238
= 108

Answer(s): 108