Joelle had four boxes, B, C, D and E which contained a total of 212 mangoes. She transferred 22 mangoes from Box B to Box C, 55 mangoes from Box C to Box D and 55 mangoes from Box D to Box E. The ratio of the number of mangoes in Box B to Box C to Box D changed from  3 : 7 : 9 to 1 : 4 : 9. How many mangoes were in Box E at first?

	Make p the same (1)x4 = (3)	B (1)	C (2)	D	E
Before	12 u	3 u	7 u	9 u	?
Change 1	- 88	- 22	+ 22
Change 2			- 55	+ 55
Change 3				- 55	+ 55
After	4 p	1 p	4 p	9 p	?

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

7 u + 22 - 55 = 4 p
7 u - 33 = 4 p --- (2)

(1) _{x 4}
12 u - 88 = 4 p --- (3)

Make p the same.

(3) = (2)
12 u - 88 = 7 u - 33
12 u - 7 u = 88 - 33
5 u = 55

1 u = 55 ÷ 5 = 11

Total number of mangoes in Box B, Box C and Box D
= 3 u + 7 u + 9 u
= 19 u

Total number of mangoes in Box E at first
= 212 - 19 u
= 212 - 19 x 11
= 212 - 209
= 3

Answer(s): 3