Natalie had four boxes, N, P, Q and R which contained a total of 266 pears. She transferred 36 pears from Box N to Box P, 89 pears from Box P to Box Q and 143 pears from Box Q to Box R. The ratio of the number of pears in Box N to Box P to Box Q changed from  4 : 7 : 10 to 1 : 3 : 7. How many pears were in Box R at first?

	Make p the same (1)x3 = (3)	N (1)	P (2)	Q	R
Before	12 u	4 u	7 u	10 u	?
Change 1	- 108	- 36	+ 36
Change 2			- 89	+ 89
Change 3				- 143	+ 143
After	3 p	1 p	3 p	7 p	?

4 u - 36 = 1 p --- (1)

7 u + 36 - 89 = 3 p
7 u - 53 = 3 p --- (2)

(1) _{x 3}
12 u - 108 = 3 p --- (3)

Make p the same.

(3) = (2)
12 u - 108 = 7 u - 53
12 u - 7 u = 108 - 53
5 u = 55

1 u = 55 ÷ 5 = 11

Total number of pears in Box N, Box P and Box Q
= 4 u + 7 u + 10 u
= 21 u

Total number of pears in Box R at first
= 266 - 21 u
= 266 - 21 x 11
= 266 - 231
= 35

Answer(s): 35