Opal had four boxes, K, L, M and N which contained a total of 223 apples. She transferred 22 apples from Box K to Box L, 56 apples from Box L to Box M and 125 apples from Box M to Box N. The ratio of the number of apples in Box K to Box L to Box M changed from  3 : 6 : 11 to 1 : 4 : 6. How many apples were in Box N at first?

	Make p the same (1)x4 = (3)	K (1)	L (2)	M	N
Before	12 u	3 u	6 u	11 u	?
Change 1	- 88	- 22	+ 22
Change 2			- 56	+ 56
Change 3				- 125	+ 125
After	4 p	1 p	4 p	6 p	?

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

6 u + 22 - 56 = 4 p
6 u - 34 = 4 p --- (2)

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

Make p the same.

(3) = (2)
12 u - 88 = 6 u - 34
12 u - 6 u = 88 - 34
6 u = 54

1 u = 54 ÷ 6 = 9

Total number of apples in Box K, Box L and Box M
= 3 u + 6 u + 11 u
= 20 u

Total number of apples in Box N at first
= 223 - 20 u
= 223 - 20 x 9
= 223 - 180
= 43

Answer(s): 43