Sabrina had four boxes, P, Q, R and S which contained a total of 270 oranges. She transferred 44 oranges from Box P to Box Q, 104 oranges from Box Q to Box R and 176 oranges from Box R to Box S. The ratio of the number of oranges in Box P to Box Q to Box R changed from  4 : 6 : 9 to 1 : 3 : 9. How many oranges were in Box S at first?

	Make p the same (1)x3 = (3)	P (1)	Q (2)	R	S
Before	12 u	4 u	6 u	9 u	?
Change 1	- 132	- 44	+ 44
Change 2			- 104	+ 104
Change 3				- 176	+ 176
After	3 p	1 p	3 p	9 p	?

4 u - 44 = 1 p --- (1)

6 u + 44 - 104 = 3 p
6 u - 60 = 3 p --- (2)

(1) _{x 3}
12 u - 132 = 3 p --- (3)

Make p the same.

(3) = (2)
12 u - 132 = 6 u - 60
12 u - 6 u = 132 - 60
6 u = 72

1 u = 72 ÷ 6 = 12

Total number of oranges in Box P, Box Q and Box R
= 4 u + 6 u + 9 u
= 19 u

Total number of oranges in Box S at first
= 270 - 19 u
= 270 - 19 x 12
= 270 - 228
= 42

Answer(s): 42