Lucy had four containers, L, M, N and P which contained a total of 276 lemons. She transferred 22 lemons from Container L to Container M, 54 lemons from Container M to Container N and 83 lemons from Container N to Container P. The ratio of the number of lemons in Container L to Container M to Container N changed from  2 : 4 : 5 to 1 : 5 : 9. How many lemons were in Container P at first?

	Make p the same (1)x5 = (3)	L (1)	M (2)	N	P
Before	10 u	2 u	4 u	5 u	?
Change 1	- 110	- 22	+ 22
Change 2			- 54	+ 54
Change 3				- 83	+ 83
After	5 p	1 p	5 p	9 p	?

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

4 u + 22 - 54 = 5 p
4 u - 32 = 5 p --- (2)

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

Make p the same.

(3) = (2)
10 u - 110 = 4 u - 32
10 u - 4 u = 110 - 32
6 u = 78

1 u = 78 ÷ 6 = 13

Total number of lemons in Container L, Container M and Container N
= 2 u + 4 u + 5 u
= 11 u

Total number of lemons in Container P at first
= 276 - 11 u
= 276 - 11 x 13
= 276 - 143
= 133

Answer(s): 133