Penelope had four boxes, A, B, C and D which contained a total of 260 pears. She transferred 12 pears from Box A to Box B, 15 pears from Box B to Box C and 9 pears from Box C to Box D. The ratio of the number of pears in Box A to Box B to Box C changed from  1 : 2 : 3 to 1 : 5 : 9. How many pears were in Box D at first?

	Make p the same (1)x5 = (3)	A (1)	B (2)	C	D
Before	5 u	1 u	2 u	3 u	?
Change 1	- 60	- 12	+ 12
Change 2			- 15	+ 15
Change 3				- 9	+ 9
After	5 p	1 p	5 p	9 p	?

1 u - 12 = 1 p --- (1)

2 u + 12 - 15 = 5 p
2 u - 3 = 5 p --- (2)

(1) _{x 5}
5 u - 60 = 5 p --- (3)

Make p the same.

(3) = (2)
5 u - 60 = 2 u - 3
5 u - 2 u = 60 - 3
3 u = 57

1 u = 57 ÷ 3 = 19

Total number of pears in Box A, Box B and Box C
= 1 u + 2 u + 3 u
= 6 u

Total number of pears in Box D at first
= 260 - 6 u
= 260 - 6 x 19
= 260 - 114
= 146

Answer(s): 146