Roshel had four boxes, G, H, J and K which contained a total of 147 pears. She transferred 11 pears from Box G to Box H, 34 pears from Box H to Box J and 53 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  3 : 7 : 11 to 1 : 3 : 9. How many pears were in Box K at first?

	Make p the same (1)x3 = (3)	G (1)	H (2)	J	K
Before	9 u	3 u	7 u	11 u	?
Change 1	- 33	- 11	+ 11
Change 2			- 34	+ 34
Change 3				- 53	+ 53
After	3 p	1 p	3 p	9 p	?

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

7 u + 11 - 34 = 3 p
7 u - 23 = 3 p --- (2)

(1) _{x 3}
9 u - 33 = 3 p --- (3)

Make p the same.

(3) = (2)
9 u - 33 = 7 u - 23
9 u - 7 u = 33 - 23
2 u = 10

1 u = 10 ÷ 2 = 5

Total number of pears in Box G, Box H and Box J
= 3 u + 7 u + 11 u
= 21 u

Total number of pears in Box K at first
= 147 - 21 u
= 147 - 21 x 5
= 147 - 105
= 42

Answer(s): 42