Roshel had four boxes, P, Q, R and S which contained a total of 279 passion fruits. She transferred 33 passion fruits from Box P to Box Q, 108 passion fruits from Box Q to Box R and 192 passion fruits from Box R to Box S. The ratio of the number of passion fruits in Box P to Box Q to Box R changed from  3 : 7 : 9 to 1 : 3 : 8. How many passion fruits were in Box S at first?

	Make p the same (1)x3 = (3)	P (1)	Q (2)	R	S
Before	9 u	3 u	7 u	9 u	?
Change 1	- 99	- 33	+ 33
Change 2			- 108	+ 108
Change 3				- 192	+ 192
After	3 p	1 p	3 p	8 p	?

3 u - 33 = 1 p --- (1)

7 u + 33 - 108 = 3 p
7 u - 75 = 3 p --- (2)

(1) _{x 3}
9 u - 99 = 3 p --- (3)

Make p the same.

(3) = (2)
9 u - 99 = 7 u - 75
9 u - 7 u = 99 - 75
2 u = 24

1 u = 24 ÷ 2 = 12

Total number of passion fruits in Box P, Box Q and Box R
= 3 u + 7 u + 9 u
= 19 u

Total number of passion fruits in Box S at first
= 279 - 19 u
= 279 - 19 x 12
= 279 - 228
= 51

Answer(s): 51