Raeann had four boxes, K, L, M and N which contained a total of 238 apples. She transferred 33 apples from Box K to Box L, 58 apples from Box L to Box M and 109 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  2 : 3 : 5 to 1 : 5 : 7. How many apples were in Box N at first?

	Make p the same (1)x5 = (3)	K (1)	L (2)	M	N
Before	10 u	2 u	3 u	5 u	?
Change 1	- 165	- 33	+ 33
Change 2			- 58	+ 58
Change 3				- 109	+ 109
After	5 p	1 p	5 p	7 p	?

2 u - 33 = 1 p --- (1)

3 u + 33 - 58 = 5 p
3 u - 25 = 5 p --- (2)

(1) _{x 5}
10 u - 165 = 5 p --- (3)

Make p the same.

(3) = (2)
10 u - 165 = 3 u - 25
10 u - 3 u = 165 - 25
7 u = 140

1 u = 140 ÷ 7 = 20

Total number of apples in Box K, Box L and Box M
= 2 u + 3 u + 5 u
= 10 u

Total number of apples in Box N at first
= 238 - 10 u
= 238 - 10 x 20
= 238 - 200
= 38

Answer(s): 38