Opal had four boxes, P, Q, R and S which contained a total of 221 apples. She transferred 22 apples from Box P to Box Q, 54 apples from Box Q to Box R and 96 apples from Box R to Box S. The ratio of the number of apples in Box P to Box Q to Box R changed from  4 : 7 : 10 to 1 : 5 : 9. How many apples were in Box S at first?

	Make p the same (1)x5 = (3)	P (1)	Q (2)	R	S
Before	20 u	4 u	7 u	10 u	?
Change 1	- 110	- 22	+ 22
Change 2			- 54	+ 54
Change 3				- 96	+ 96
After	5 p	1 p	5 p	9 p	?

4 u - 22 = 1 p --- (1)

7 u + 22 - 54 = 5 p
7 u - 32 = 5 p --- (2)

(1) _{x 5}
20 u - 110 = 5 p --- (3)

Make p the same.

(3) = (2)
20 u - 110 = 7 u - 32
20 u - 7 u = 110 - 32
13 u = 78

1 u = 78 ÷ 13 = 6

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

Total number of apples in Box S at first
= 221 - 21 u
= 221 - 21 x 6
= 221 - 126
= 95

Answer(s): 95