Emily had four boxes, P, Q, R and S which contained a total of 260 persimmons. She transferred 18 persimmons from Box P to Box Q, 45 persimmons from Box Q to Box R and 72 persimmons from Box R to Box S. The ratio of the number of persimmons in Box P to Box Q to Box R changed from  3 : 7 : 10 to 1 : 4 : 7. How many persimmons were in Box S at first?

	Make p the same (1)x4 = (3)	P (1)	Q (2)	R	S
Before	12 u	3 u	7 u	10 u	?
Change 1	- 72	- 18	+ 18
Change 2			- 45	+ 45
Change 3				- 72	+ 72
After	4 p	1 p	4 p	7 p	?

3 u - 18 = 1 p --- (1)

7 u + 18 - 45 = 4 p
7 u - 27 = 4 p --- (2)

(1) _{x 4}
12 u - 72 = 4 p --- (3)

Make p the same.

(3) = (2)
12 u - 72 = 7 u - 27
12 u - 7 u = 72 - 27
5 u = 45

1 u = 45 ÷ 5 = 9

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

Total number of persimmons in Box S at first
= 260 - 20 u
= 260 - 20 x 9
= 260 - 180
= 80

Answer(s): 80