Victoria had four boxes, U, V, W and X which contained a total of 207 pears. She transferred 10 pears from Box U to Box V, 36 pears from Box V to Box W and 77 pears from Box W to Box X. The ratio of the number of pears in Box U to Box V to Box W changed from  2 : 6 : 11 to 1 : 4 : 9. How many pears were in Box X at first?

	Make p the same (1)x4 = (3)	U (1)	V (2)	W	X
Before	8 u	2 u	6 u	11 u	?
Change 1	- 40	- 10	+ 10
Change 2			- 36	+ 36
Change 3				- 77	+ 77
After	4 p	1 p	4 p	9 p	?

2 u - 10 = 1 p --- (1)

6 u + 10 - 36 = 4 p
6 u - 26 = 4 p --- (2)

(1) _{x 4}
8 u - 40 = 4 p --- (3)

Make p the same.

(3) = (2)
8 u - 40 = 6 u - 26
8 u - 6 u = 40 - 26
2 u = 14

1 u = 14 ÷ 2 = 7

Total number of pears in Box U, Box V and Box W
= 2 u + 6 u + 11 u
= 19 u

Total number of pears in Box X at first
= 207 - 19 u
= 207 - 19 x 7
= 207 - 133
= 74

Answer(s): 74