Irene had four boxes, L, M, N and P which contained a total of 204 starfruits. She transferred 19 starfruits from Box L to Box M, 29 starfruits from Box M to Box N and 48 starfruits from Box N to Box P. The ratio of the number of starfruits in Box L to Box M to Box N changed from  4 : 5 : 9 to 1 : 4 : 7. How many starfruits were in Box P at first?

	Make p the same (1)x4 = (3)	L (1)	M (2)	N	P
Before	16 u	4 u	5 u	9 u	?
Change 1	- 76	- 19	+ 19
Change 2			- 29	+ 29
Change 3				- 48	+ 48
After	4 p	1 p	4 p	7 p	?

4 u - 19 = 1 p --- (1)

5 u + 19 - 29 = 4 p
5 u - 10 = 4 p --- (2)

(1) _{x 4}
16 u - 76 = 4 p --- (3)

Make p the same.

(3) = (2)
16 u - 76 = 5 u - 10
16 u - 5 u = 76 - 10
11 u = 66

1 u = 66 ÷ 11 = 6

Total number of starfruits in Box L, Box M and Box N
= 4 u + 5 u + 9 u
= 18 u

Total number of starfruits in Box P at first
= 204 - 18 u
= 204 - 18 x 6
= 204 - 108
= 96

Answer(s): 96