Penelope had four boxes, U, V, W and X which contained a total of 235 kiwis. She transferred 37 kiwis from Box U to Box V, 75 kiwis from Box V to Box W and 164 kiwis from Box W to Box X. The ratio of the number of kiwis in Box U to Box V to Box W changed from  4 : 5 : 11 to 1 : 4 : 7. How many kiwis were in Box X at first?

	Make p the same (1)x4 = (3)	U (1)	V (2)	W	X
Before	16 u	4 u	5 u	11 u	?
Change 1	- 148	- 37	+ 37
Change 2			- 75	+ 75
Change 3				- 164	+ 164
After	4 p	1 p	4 p	7 p	?

4 u - 37 = 1 p --- (1)

5 u + 37 - 75 = 4 p
5 u - 38 = 4 p --- (2)

(1) _{x 4}
16 u - 148 = 4 p --- (3)

Make p the same.

(3) = (2)
16 u - 148 = 5 u - 38
16 u - 5 u = 148 - 38
11 u = 110

1 u = 110 ÷ 11 = 10

Total number of kiwis in Box U, Box V and Box W
= 4 u + 5 u + 11 u
= 20 u

Total number of kiwis in Box X at first
= 235 - 20 u
= 235 - 20 x 10
= 235 - 200
= 35

Answer(s): 35