Risa had four containers, U, V, W and X which contained a total of 316 lemons. She transferred 41 lemons from Container U to Container V, 76 lemons from Container V to Container W and 169 lemons from Container W to Container X. The ratio of the number of lemons in Container U to Container V to Container W changed from  3 : 5 : 9 to 1 : 5 : 6. How many lemons were in Container X at first?

	Make p the same (1)x5 = (3)	U (1)	V (2)	W	X
Before	15 u	3 u	5 u	9 u	?
Change 1	- 205	- 41	+ 41
Change 2			- 76	+ 76
Change 3				- 169	+ 169
After	5 p	1 p	5 p	6 p	?

3 u - 41 = 1 p --- (1)

5 u + 41 - 76 = 5 p
5 u - 35 = 5 p --- (2)

(1) _{x 5}
15 u - 205 = 5 p --- (3)

Make p the same.

(3) = (2)
15 u - 205 = 5 u - 35
15 u - 5 u = 205 - 35
10 u = 170

1 u = 170 ÷ 10 = 17

Total number of lemons in Container U, Container V and Container W
= 3 u + 5 u + 9 u
= 17 u

Total number of lemons in Container X at first
= 316 - 17 u
= 316 - 17 x 17
= 316 - 289
= 27

Answer(s): 27