Roshel had four boxes, R, S, T and U which contained a total of 314 chikoos. She transferred 13 chikoos from Box R to Box S, 29 chikoos from Box S to Box T and 38 chikoos from Box T to Box U. The ratio of the number of chikoos in Box R to Box S to Box T changed from  4 : 7 : 9 to 1 : 4 : 9. How many chikoos were in Box U at first?

	Make p the same (1)x4 = (3)	R (1)	S (2)	T	U
Before	16 u	4 u	7 u	9 u	?
Change 1	- 52	- 13	+ 13
Change 2			- 29	+ 29
Change 3				- 38	+ 38
After	4 p	1 p	4 p	9 p	?

4 u - 13 = 1 p --- (1)

7 u + 13 - 29 = 4 p
7 u - 16 = 4 p --- (2)

(1) _{x 4}
16 u - 52 = 4 p --- (3)

Make p the same.

(3) = (2)
16 u - 52 = 7 u - 16
16 u - 7 u = 52 - 16
9 u = 36

1 u = 36 ÷ 9 = 4

Total number of chikoos in Box R, Box S and Box T
= 4 u + 7 u + 9 u
= 20 u

Total number of chikoos in Box U at first
= 314 - 20 u
= 314 - 20 x 4
= 314 - 80
= 234

Answer(s): 234