Jane had four boxes, M, N, P and Q which contained a total of 318 kiwis. She transferred 49 kiwis from Box M to Box N, 84 kiwis from Box N to Box P and 210 kiwis from Box P to Box Q. The ratio of the number of kiwis in Box M to Box N to Box P changed from  4 : 5 : 12 to 1 : 5 : 6. How many kiwis were in Box Q at first?

	Make p the same (1)x5 = (3)	M (1)	N (2)	P	Q
Before	20 u	4 u	5 u	12 u	?
Change 1	- 245	- 49	+ 49
Change 2			- 84	+ 84
Change 3				- 210	+ 210
After	5 p	1 p	5 p	6 p	?

4 u - 49 = 1 p --- (1)

5 u + 49 - 84 = 5 p
5 u - 35 = 5 p --- (2)

(1) _{x 5}
20 u - 245 = 5 p --- (3)

Make p the same.

(3) = (2)
20 u - 245 = 5 u - 35
20 u - 5 u = 245 - 35
15 u = 210

1 u = 210 ÷ 15 = 14

Total number of kiwis in Box M, Box N and Box P
= 4 u + 5 u + 12 u
= 21 u

Total number of kiwis in Box Q at first
= 318 - 21 u
= 318 - 21 x 14
= 318 - 294
= 24

Answer(s): 24