Gabby had four boxes, A, B, C and D which contained a total of 226 lemons. She transferred 14 lemons from Box A to Box B, 38 lemons from Box B to Box C and 66 lemons from Box C to Box D. The ratio of the number of lemons in Box A to Box B to Box C changed from  3 : 8 : 11 to 1 : 4 : 6. How many lemons were in Box D at first?

	Make p the same (1)x4 = (3)	A (1)	B (2)	C	D
Before	12 u	3 u	8 u	11 u	?
Change 1	- 56	- 14	+ 14
Change 2			- 38	+ 38
Change 3				- 66	+ 66
After	4 p	1 p	4 p	6 p	?

3 u - 14 = 1 p --- (1)

8 u + 14 - 38 = 4 p
8 u - 24 = 4 p --- (2)

(1) _{x 4}
12 u - 56 = 4 p --- (3)

Make p the same.

(3) = (2)
12 u - 56 = 8 u - 24
12 u - 8 u = 56 - 24
4 u = 32

1 u = 32 ÷ 4 = 8

Total number of lemons in Box A, Box B and Box C
= 3 u + 8 u + 11 u
= 22 u

Total number of lemons in Box D at first
= 226 - 22 u
= 226 - 22 x 8
= 226 - 176
= 50

Answer(s): 50