Penelope had four containers, C, D, E and F which contained a total of 160 pears. She transferred 22 pears from Container C to Container D, 41 pears from Container D to Container E and 82 pears from Container E to Container F. The ratio of the number of pears in Container C to Container D to Container E changed from  2 : 3 : 5 to 1 : 5 : 6. How many pears were in Container F at first?

	Make p the same (1)x5 = (3)	C (1)	D (2)	E	F
Before	10 u	2 u	3 u	5 u	?
Change 1	- 110	- 22	+ 22
Change 2			- 41	+ 41
Change 3				- 82	+ 82
After	5 p	1 p	5 p	6 p	?

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

3 u + 22 - 41 = 5 p
3 u - 19 = 5 p --- (2)

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

Make p the same.

(3) = (2)
10 u - 110 = 3 u - 19
10 u - 3 u = 110 - 19
7 u = 91

1 u = 91 ÷ 7 = 13

Total number of pears in Container C, Container D and Container E
= 2 u + 3 u + 5 u
= 10 u

Total number of pears in Container F at first
= 160 - 10 u
= 160 - 10 x 13
= 160 - 130
= 30

Answer(s): 30