Abi had four boxes, N, P, Q and R which contained a total of 262 starfruits. She transferred 10 starfruits from Box N to Box P, 30 starfruits from Box P to Box Q and 54 starfruits from Box Q to Box R. The ratio of the number of starfruits in Box N to Box P to Box Q changed from  3 : 7 : 10 to 1 : 4 : 8. How many starfruits were in Box R at first?

	Make p the same (1)x4 = (3)	N (1)	P (2)	Q	R
Before	12 u	3 u	7 u	10 u	?
Change 1	- 40	- 10	+ 10
Change 2			- 30	+ 30
Change 3				- 54	+ 54
After	4 p	1 p	4 p	8 p	?

3 u - 10 = 1 p --- (1)

7 u + 10 - 30 = 4 p
7 u - 20 = 4 p --- (2)

(1) _{x 4}
12 u - 40 = 4 p --- (3)

Make p the same.

(3) = (2)
12 u - 40 = 7 u - 20
12 u - 7 u = 40 - 20
5 u = 20

1 u = 20 ÷ 5 = 4

Total number of starfruits in Box N, Box P and Box Q
= 3 u + 7 u + 10 u
= 20 u

Total number of starfruits in Box R at first
= 262 - 20 u
= 262 - 20 x 4
= 262 - 80
= 182

Answer(s): 182