Hilda had four containers, M, N, P and Q which contained a total of 349 starfruits. She transferred 39 starfruits from Container M to Container N, 52 starfruits from Container N to Container P and 84 starfruits from Container P to Container Q. The ratio of the number of starfruits in Container M to Container N to Container P changed from  4 : 7 : 12 to 1 : 5 : 8. How many starfruits were in Container Q at first?

	Make p the same (1)x5 = (3)	M (1)	N (2)	P	Q
Before	20 u	4 u	7 u	12 u	?
Change 1	- 195	- 39	+ 39
Change 2			- 52	+ 52
Change 3				- 84	+ 84
After	5 p	1 p	5 p	8 p	?

4 u - 39 = 1 p --- (1)

7 u + 39 - 52 = 5 p
7 u - 13 = 5 p --- (2)

(1) _{x 5}
20 u - 195 = 5 p --- (3)

Make p the same.

(3) = (2)
20 u - 195 = 7 u - 13
20 u - 7 u = 195 - 13
13 u = 182

1 u = 182 ÷ 13 = 14

Total number of starfruits in Container M, Container N and Container P
= 4 u + 7 u + 12 u
= 23 u

Total number of starfruits in Container Q at first
= 349 - 23 u
= 349 - 23 x 14
= 349 - 322
= 27

Answer(s): 27