Sarah had four containers, B, C, D and E which contained a total of 258 apples. She transferred 11 apples from Container B to Container C, 13 apples from Container C to Container D and 3 apples from Container D to Container E. The ratio of the number of apples in Container B to Container C to Container D changed from  3 : 6 : 10 to 1 : 4 : 8. How many apples were in Container E at first?

	Make p the same (1)x4 = (3)	B (1)	C (2)	D	E
Before	12 u	3 u	6 u	10 u	?
Change 1	- 44	- 11	+ 11
Change 2			- 13	+ 13
Change 3				- 3	+ 3
After	4 p	1 p	4 p	8 p	?

3 u - 11 = 1 p --- (1)

6 u + 11 - 13 = 4 p
6 u - 2 = 4 p --- (2)

(1) _{x 4}
12 u - 44 = 4 p --- (3)

Make p the same.

(3) = (2)
12 u - 44 = 6 u - 2
12 u - 6 u = 44 - 2
6 u = 42

1 u = 42 ÷ 6 = 7

Total number of apples in Container B, Container C and Container D
= 3 u + 6 u + 10 u
= 19 u

Total number of apples in Container E at first
= 258 - 19 u
= 258 - 19 x 7
= 258 - 133
= 125

Answer(s): 125