Rachel had four containers, Q, R, S and T which contained a total of 289 lemons. She transferred 22 lemons from Container Q to Container R, 26 lemons from Container R to Container S and 46 lemons from Container S to Container T. The ratio of the number of lemons in Container Q to Container R to Container S changed from  3 : 6 : 10 to 1 : 4 : 6. How many lemons were in Container T at first?

	Make p the same (1)x4 = (3)	Q (1)	R (2)	S	T
Before	12 u	3 u	6 u	10 u	?
Change 1	- 88	- 22	+ 22
Change 2			- 26	+ 26
Change 3				- 46	+ 46
After	4 p	1 p	4 p	6 p	?

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

6 u + 22 - 26 = 4 p
6 u - 4 = 4 p --- (2)

(1) _{x 4}
12 u - 88 = 4 p --- (3)

Make p the same.

(3) = (2)
12 u - 88 = 6 u - 4
12 u - 6 u = 88 - 4
6 u = 84

1 u = 84 ÷ 6 = 14

Total number of lemons in Container Q, Container R and Container S
= 3 u + 6 u + 10 u
= 19 u

Total number of lemons in Container T at first
= 289 - 19 u
= 289 - 19 x 14
= 289 - 266
= 23

Answer(s): 23