Nora had four boxes, C, D, E and F which contained a total of 214 mangoes. She transferred 22 mangoes from Box C to Box D, 42 mangoes from Box D to Box E and 52 mangoes from Box E to Box F. The ratio of the number of mangoes in Box C to Box D to Box E changed from  4 : 5 : 10 to 1 : 2 : 7. How many mangoes were in Box F at first?

	Make p the same (1)x2 = (3)	C (1)	D (2)	E	F
Before	8 u	4 u	5 u	10 u	?
Change 1	- 44	- 22	+ 22
Change 2			- 42	+ 42
Change 3				- 52	+ 52
After	2 p	1 p	2 p	7 p	?

4 u - 22 = 1 p --- (1)

5 u + 22 - 42 = 2 p
5 u - 20 = 2 p --- (2)

(1) _{x 2}
8 u - 44 = 2 p --- (3)

Make p the same.

(3) = (2)
8 u - 44 = 5 u - 20
8 u - 5 u = 44 - 20
3 u = 24

1 u = 24 ÷ 3 = 8

Total number of mangoes in Box C, Box D and Box E
= 4 u + 5 u + 10 u
= 19 u

Total number of mangoes in Box F at first
= 214 - 19 u
= 214 - 19 x 8
= 214 - 152
= 62

Answer(s): 62