Shannon had four boxes, G, H, J and K which contained a total of 226 pears. She transferred 20 pears from Box G to Box H, 48 pears from Box H to Box J and 78 pears from Box J to Box K. The ratio of the number of pears in Box G to Box H to Box J changed from  4 : 8 : 9 to 1 : 5 : 6. How many pears were in Box K at first?

	Make p the same (1)x5 = (3)	G (1)	H (2)	J	K
Before	20 u	4 u	8 u	9 u	?
Change 1	- 100	- 20	+ 20
Change 2			- 48	+ 48
Change 3				- 78	+ 78
After	5 p	1 p	5 p	6 p	?

4 u - 20 = 1 p --- (1)

8 u + 20 - 48 = 5 p
8 u - 28 = 5 p --- (2)

(1) _{x 5}
20 u - 100 = 5 p --- (3)

Make p the same.

(3) = (2)
20 u - 100 = 8 u - 28
20 u - 8 u = 100 - 28
12 u = 72

1 u = 72 ÷ 12 = 6

Total number of pears in Box G, Box H and Box J
= 4 u + 8 u + 9 u
= 21 u

Total number of pears in Box K at first
= 226 - 21 u
= 226 - 21 x 6
= 226 - 126
= 100

Answer(s): 100