Penelope had four containers, U, V, W and X which contained a total of 348 pears. She transferred 17 pears from Container U to Container V, 45 pears from Container V to Container W and 84 pears from Container W to Container X. The ratio of the number of pears in Container U to Container V to Container W changed from  3 : 7 : 11 to 1 : 4 : 7. How many pears were in Container X at first?

	Make p the same (1)x4 = (3)	U (1)	V (2)	W	X
Before	12 u	3 u	7 u	11 u	?
Change 1	- 68	- 17	+ 17
Change 2			- 45	+ 45
Change 3				- 84	+ 84
After	4 p	1 p	4 p	7 p	?

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

7 u + 17 - 45 = 4 p
7 u - 28 = 4 p --- (2)

(1) _{x 4}
12 u - 68 = 4 p --- (3)

Make p the same.

(3) = (2)
12 u - 68 = 7 u - 28
12 u - 7 u = 68 - 28
5 u = 40

1 u = 40 ÷ 5 = 8

Total number of pears in Container U, Container V and Container W
= 3 u + 7 u + 11 u
= 21 u

Total number of pears in Container X at first
= 348 - 21 u
= 348 - 21 x 8
= 348 - 168
= 180

Answer(s): 180