Lynn had four boxes, G, H, J and K which contained a total of 158 apples. She transferred 17 apples from Box G to Box H, 43 apples from Box H to Box J and 74 apples from Box J to Box K. The ratio of the number of apples in Box G to Box H to Box J changed from  4 : 7 : 11 to 1 : 3 : 8. How many apples were in Box K at first?

	Make p the same (1)x3 = (3)	G (1)	H (2)	J	K
Before	12 u	4 u	7 u	11 u	?
Change 1	- 51	- 17	+ 17
Change 2			- 43	+ 43
Change 3				- 74	+ 74
After	3 p	1 p	3 p	8 p	?

4 u - 17 = 1 p --- (1)

7 u + 17 - 43 = 3 p
7 u - 26 = 3 p --- (2)

(1) _{x 3}
12 u - 51 = 3 p --- (3)

Make p the same.

(3) = (2)
12 u - 51 = 7 u - 26
12 u - 7 u = 51 - 26
5 u = 25

1 u = 25 ÷ 5 = 5

Total number of apples in Box G, Box H and Box J
= 4 u + 7 u + 11 u
= 22 u

Total number of apples in Box K at first
= 158 - 22 u
= 158 - 22 x 5
= 158 - 110
= 48

Answer(s): 48