Kathy had four containers, C, D, E and F which contained a total of 342 oranges. She transferred 10 oranges from Container C to Container D, 20 oranges from Container D to Container E and 52 oranges from Container E to Container F. The ratio of the number of oranges in Container C to Container D to Container E changed from  2 : 5 : 10 to 1 : 5 : 8. How many oranges were in Container F at first?

	Make p the same (1)x5 = (3)	C (1)	D (2)	E	F
Before	10 u	2 u	5 u	10 u	?
Change 1	- 50	- 10	+ 10
Change 2			- 20	+ 20
Change 3				- 52	+ 52
After	5 p	1 p	5 p	8 p	?

2 u - 10 = 1 p --- (1)

5 u + 10 - 20 = 5 p
5 u - 10 = 5 p --- (2)

(1) _{x 5}
10 u - 50 = 5 p --- (3)

Make p the same.

(3) = (2)
10 u - 50 = 5 u - 10
10 u - 5 u = 50 - 10
5 u = 40

1 u = 40 ÷ 5 = 8

Total number of oranges in Container C, Container D and Container E
= 2 u + 5 u + 10 u
= 17 u

Total number of oranges in Container F at first
= 342 - 17 u
= 342 - 17 x 8
= 342 - 136
= 206

Answer(s): 206