Jaslyn had four boxes, P, Q, R and S which contained a total of 292 mangosteens. She transferred 22 mangosteens from Box P to Box Q, 76 mangosteens from Box Q to Box R and 138 mangosteens from Box R to Box S. The ratio of the number of mangosteens in Box P to Box Q to Box R changed from  3 : 8 : 10 to 1 : 5 : 9. How many mangosteens were in Box S at first?

	Make p the same (1)x5 = (3)	P (1)	Q (2)	R	S
Before	15 u	3 u	8 u	10 u	?
Change 1	- 110	- 22	+ 22
Change 2			- 76	+ 76
Change 3				- 138	+ 138
After	5 p	1 p	5 p	9 p	?

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

8 u + 22 - 76 = 5 p
8 u - 54 = 5 p --- (2)

(1) _{x 5}
15 u - 110 = 5 p --- (3)

Make p the same.

(3) = (2)
15 u - 110 = 8 u - 54
15 u - 8 u = 110 - 54
7 u = 56

1 u = 56 ÷ 7 = 8

Total number of mangosteens in Box P, Box Q and Box R
= 3 u + 8 u + 10 u
= 21 u

Total number of mangosteens in Box S at first
= 292 - 21 u
= 292 - 21 x 8
= 292 - 168
= 124

Answer(s): 124